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Trigonometry Mixed Review: Part 1>
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Question 1 of 8
1. Question
Solve for θRound your answer to the nearest minute- θ= (35)° (55)′
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Sin Ratio
sin=oppositehypotenuseCos Ratio
cos=adjacenthypotenuseTan Ratio
tan=oppositeadjacentFirst we need to identify which trig ratio to use.One of the known lengths (29) is adjacent to θ and the other length (21) is opposite to θHence, we can use the tanratio to solve for θtanθ = oppositeadjacent tanratio tanθ = 2129 Plug in the values tanθ = 0.724 Use the inverse function for tan on your calculator to get θ by itselfθ = tan-1(0.724) The inverse of tan is tan-1 θ = 35.9097 Use the shift tan function on your calculator θ = 35°54’ Use the \text(degrees) function on your calculator theta = 35°55’ Rounded to the nearest minute theta=35°55’ -
Question 2 of 8
2. Question
Solve for xRound your answer to one decimal place- x = (25.3)
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Sin Ratio
sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}Cos Ratio
cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}Tan Ratio
tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}First we need to identify which trig ratio to use.One of the known angles (56°) has 21 as an \text(opposite) side and x is the \text(hypotenuse)Hence, we can use the sin \text(ratio) to solve for xsin theta = \frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}} sin \text(ratio) sin (56°) = \frac{\color{#004ec4}{21}}{\color{#e85e00}{x}} Plug in the values Get x by itself to find its valuesin (56°) = 21/x x xx sin (56°) = 21 Multiply both sides by x x = 21/sin (56°) Divide both sides by sin(56°) x = 21/0.8290375726 Evaluate sin(56°) on the calculator x = 25.3 Round to one decimal place x=25.3 -
Question 3 of 8
3. Question
Solve for thetaRound your answer to the nearest degree- theta= (73)°
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Sin Ratio
sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}Cos Ratio
cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}Tan Ratio
tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}First we need to identify which trig ratio to use.One of the known lengths (8) is \text(adjacent) to theta and the other length (28) is the \text(hypotenuse)Hence, we can use the cos \text(ratio) to solve for thetacos theta = \frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}} cos \text(ratio) cos theta = \frac{\color{#00880a}{8}}{\color{#e85e00}{28}} Plug in the values cos theta = 0.286 Use the inverse function for cos on your calculator to get theta by itselftheta = cos^(-1) (0.286) The inverse of cos is cos^(-1) theta = 73.381° Use the \text(shift) cos function on your calculator theta = 73° Rounded to the nearest degree theta=73° -
Question 4 of 8
4. Question
Find the length of dThe given measurements are in metresRound your answer to the nearest whole number- d= (139) m
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The Angles of Elevation and Depression are the angles created by the upward or downward slope of the hypotenuse.The lines on top and bottom of the building are parallel, and the hypotenuse that cuts through it creates an angle of depression measured 47°10’Since the angle of elevation (theta) is opposite of the angle of depression
(47°10’), theta is also equal to 47°10’Next, we need to identify which trig ratio to use.Angle theta has 150 m as an \text(opposite) side and d as an \text(adjacent) side.Hence, we can use the tan \text(ratio) to solve for dtantheta = \frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}} tan \text(ratio) tan47˚10’ = \frac{\color{#004ec4}{150}}{\color{#00880a}{d}} Plug in the values d xx 1.0786 = 150 Cross multiply d = 150/1.0786 Divide 1.0786 from both sides to isolate d d = 139 m d=139 m -
Question 5 of 8
5. Question
Find the area of the TriangleThe given measurements are in unitsRound your answer to one decimal place- \text(Area )= (32.6)units^2
Correct
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Area of a Triangle Formula
\text(Area )=1/2 xxbtimesctimes sinARemember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
Solve for the area using the Area of a Triangle formulaA = 1/2 xxbtimesctimes sinA Area of a Triangle formula = 1/2 xx11.5times7times sin126° Plug in the known lengths = 32.6 units^2 Rounded to one decimal place The given measurements are in units, so the area is measured as square units\text(Area)=32.6 units^2 -
Question 6 of 8
6. Question
Solve for thetaRound your answer to the nearest minute- 1.
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Hint
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Subtitles- subtitles off
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- English
Chapters- Chapters
Sin Ratio
sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}Cos Ratio
cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}Tan Ratio
tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}First we need to identify which trig ratio to use.One of the known lengths (4.9) is \text(opposite) to theta, and the other length (10.6) is \text(adjacent) to theta, but we only need half of that length to form a right triangle.\text(adjacent) = 10.6divide2 \text(adjacent) = 5.3 Hence, we can use the tan \text(ratio) to solve for thetatan theta = \frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}} tan \text(ratio) tan theta = \frac{\color{#004ec4}{4.9}}{\color{#00880a}{5.3}} Plug in the values tan theta = 0.9243 Use the inverse function for tan on your calculator to get theta by itselftheta = tan^(-1) (0.9243) The inverse of tan is tan^(-1) theta = 42.7543 Use the \text(shift) tan function on your calculator theta = 42°45’15” Use the \text(degrees) function on your calculator theta = 42°45’ Rounded to the nearest minute theta=42°45’ -
Question 7 of 8
7. Question
Find the area of the TriangleThe given measurements are in unitsRound your answer to the nearest whole number- \text(Area )= (47)units^2
Correct
Correct!
Incorrect
Area of a Triangle Formula
\text(Area )=1/2 xxatimesctimes sinBRemember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
First, we need to find an angle between two sides with known values.We can use the Sine Rule to find angle Ca/sinA = c/sinC Sine Rule Formula 14/(sin77°) = 7/sinC Plug in the values sinC xx 14 = 7 xx sin77° Cross multiply sinC = (7 xx sin77°)/14 Divide 14 from each side to isolate sinC sinC = 6.821/14 Simplify sinC = 0.487 Use the inverse function for sin on your calculator to get C by itselfC = sin^-1(0.487) The inverse of sin is sin^-1 C = 29.155 Use the shift sin function on your calculator C = 29.2° Rounded to one decimal place Now that we have the value of C, we can get the value of B by subtracting the total value of A and C to 180°, the total interior angle of a triangleB = 180°-(A+C) B = 180°-(77+29.2) Plug in the known values B = 73.8° Finally, solve for the area using the Area of a Triangle formula\text(Area) = 1/2 xxatimesctimes sinB Area of a Triangle formula = 1/2 xx14times7times sin73.8° Plug in the known lengths = 47.0 units^2 Rounded to one decimal place The given measurements are in units, so the area is measured as square units\text(Area)=47 units^2 -
Question 8 of 8
8. Question
Find the area of the TriangleThe given measurements are in unitsRound your answer to the nearest whole number- \text(Area )= (92)units^2
Correct
Great Work!
Incorrect
Area of a Triangle Formula
\text(Area )=1/2 xxbtimesctimes sinACosine Rule (finding an angle)
cos\color{#004ec4}{A}=\frac{\color{#00880a}{b^2}+\color{#e85e00}{c^2}-\color{#004ec4}{a^2}}{2\color{#00880a}{b}\color{#e85e00}{c}}Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
First, we need to find an angle to use for the Area of a Triangle formulaWe can use the Cosine Rule (finding an angle) to solve for AcosA = \frac{\color{#00880a}{b^2}+\color{#e85e00}{c^2}-\color{#004ec4}{a^2}}{2\color{#00880a}{b}\color{#e85e00}{c}} Cosine Rule Formula cosA = \frac{\color{#00880a}{13.9^2}+\color{#e85e00}{14^2}-\color{#004ec4}{16^2}}{2\color{#00880a}{(13.9)}\color{#e85e00}{(14)}} Plug in known values cosA = (193.21+196-256)/(389.2) Evaluate cosA = 0.342 Use the inverse function for cos on your calculator to get A by itselfA = cos^-1(0.342) The inverse of cos is cos^-1 A = 71.094 Use the shift cos function on your calculator A = 71.1° Rounded to one decimal place Finally, solve for the area using the Area of a Triangle formulaA = 1/2 xxbtimesctimes sinA Area of a Triangle formula = 1/2 xx13.9times14times sin71.1° Plug in the known lengths = 92 units^2 Rounded to one decimal place The given measurements are in units, so the area is measured as square units\text(Area)=92 units^2
Quizzes
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Sine Rule: Solving for a Side
- Sine Rule: Solving for an Angle
- Cosine Rule: Solving for a Side
- Cosine Rule: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)