Right Triangle Relationships and Trigonometry REVIEW

Given right triangle DEF, what is the value of sin(E)?

3/5

Which equation can be used to find the length of AC?

(10)sin(40o) = AC

What is the length of AC? Round to the nearest tenth.

10.5 m

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

acute, because 102+122>152

Use the diagram to complete the statement. Given △JKL, sin(38°) equals

cos(52°).

Which equation can be used to find the measure of angle LJK?

cos(x) = 10/15

Which trigonometric ratios are correct for triangle ABC? Check all that apply.

sin(C) = √3/2 tan(C) = √3 sin(B) = 1/2

In which triangle is the value of x equal to tan−1(3.1/5.2)?

D

Given △DEF, which is not equal to cos(F)?

tan(F).

What is the approximate value of x? Round to the nearest tenth.

4.6 cm

Which is the best approximation for the measure of angle EGF?

40.2°

Given right triangle DEF, what is the value of tan(F)?

40/9

The equation tan−1(8.9/7.7) = x can be used to find the measure of angle LKJ. What is the measure of angle LKJ? Round to the nearest whole degree.

49

Given right triangle JKL, what is the value of cos(L)?

5/13

Which statements are true about triangle QRS? Check all that apply.

The side opposite ∠Q is RS The hypotenuse is QR. The side adjacent to ∠Q is QS.

Given right triangle ABC, what is the value of tan(A)?

12/5

A right triangle has one angle that measure 23°. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.

161.7 cm2

What is the approximate value of y − x?

17.2°

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown. What is the smallest possible whole-number length of the unknown side?

19 inches

The equation sin(25°) = 9/c can be used to find the length of AB. What is the length of AB? Round to the nearest tenth.

21.3 in.

An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

24.2 cm

What is the length of AB? Round to the nearest tenth.

38.6 m

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

39.4°

Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown. If the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox?

a quadrilateral, because angle C and angle X are acute

Triangle ABC is a right triangle and cos(22.6°)= b/13. Solve for b and round to the nearest whole number. Which equation correctly uses the value of b to solve for a?

tan(22.6°) = a/12