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Geometry/Trig
Lesson 13-7: Final Exam Review 7
[Unit 10: Right Triangle Trig]
Name: ______________________________
Date: _______________________________
Learning Goals Covered in this Unit
(1) How do we label sides of right triangles with respect to a given angle? (2) What are trigonometric ratios and how can
we use them to solve for side and angles? (3) How can we use auxiliary lines to solve problems involving non-right triangles?
Trigonometric Ratios – SOHCAHTOA ****PUT CALCULATOR IN _______________________***
-
Used to solve for sides or to solve for angles
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When solving for a __________ remember to use: sine, cosine, or tangent and cross multiply!
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When solving for an __________ remember to use: inverse sine, inverse cosine, or inverse tangent
1ex) sin-1(sin𝜃) =
4
sin-1( )
5
4
sin-1(sin𝜃) = sin-1( )
5
𝜃 = 53.1°
*Angle of Elevation – angle formed from ground up
*Angle of Depression – angle formed from eye-level down
Auxiliary lines to solve in non-right triangles
Tips:
 Read carefully! If it is NOT a right triangle we CANNOT use SOHCAHTOA!
 Auxiliary lines will always be an ALTITUDE to help us get right triangles so we CAN use SOHCAHTOA
 Must ADD the two pieces that you have found together, to find the missing side.
Try it! Sketch in an auxiliary line to help create right triangles in the diagram below:
Geometry/Trig
Your Turn!
1. In triangle MCT, the measure of
sine of
? (Hint: DRAW IT!)
1)
,
,
, and
. Which ratio represents the
2)
3)
4)
2. The diagram below shows right triangle LMP.
Which ratio represents the tangent of
?
1)
2)
3)
4)
3. Which equation shows a correct trigonometric ratio for angle A in the right triangle below?
1)
2)
3)
4)
Geometry/Trig
4. Solve for the value of x, to the nearest tenth.
5. Solve for the length of side y. Round your answer to the nearest whole number.
6. You are standing 15 feet away from the base of a flagpole. The angle of elevation from you to the top of the
flagpole is 36°. How tall is the flagpole to the nearest foot?
7. A ladder is resting against the side of a building. The bottom of the ladder is 12 feet from the building, and the
ladder reaches 7 feet up the side of the building. Find the measure of the angle of elevation, to the nearest
tenth of a degree.
Geometry/Trig
8. In right triangle ABC, leg BC=15 and leg AC=20. Find angle A to the nearest degree.
9. Given triangle 𝐷𝐸𝐹, ∠𝐸 = 67°, ∠𝐹 = 91°, 𝐷𝐹 = 16.55, and 𝐸𝐹 = 6.74,
a. Calculate the measure of angle D and write your answer in the diagram.
b.
Find 𝐷𝐸 to the nearest hundredth using an auxiliary line.
10. Solve for the 𝑚∡𝐵 to the nearest hundredth of a degree.
Geometry/Trig
11. Given the following diagram solve for line segment LN to the nearest 100th using an auxiliary line. .