Chapter 7.7 Notes: Solve Right Triangles

Goal: You will use inverse tangent, sine, and cosine ratios to determine the unknown angle measures of right triangles and use tangent, cosine, and sine ratios to determine unknown side lengths of right triangles.

• To solve a right triangle means to find the measures of all of its sides and angles.

• You can solve a right triangle if you know either of the following:

– Two side lengths

– One side length and the measure of one acute angle.

Using the Inverse Tangent Function:

• Use the inverse tangent, also called the arc tangent (tan-1) to find the measure of an acute angle of a right triangle.

• On the calculator, you will use the 2nd key (tan-1).

Ex.1: Find to the nearest degree.

a. tan M = 0.5

b. tan M = 0.34

c. tan M = 100

M

Ex.2: Find the measure of and to the nearest tenth.

Using the Inverse Sine and Cosine Ratios:

• To find the measure of an acute angle of a right triangle, you will use the inverse sine or arc sine (sin-1) or inverse cosine or arc cosine (cos-1).

• On the calculator, you will use the 2nd key (sin-1 or cos-1).

A C

Ex.3: Find the measure of and to the nearest degree.

a. sin A = 0.87

b. cos B = 0.15

c. sin A = 0.75

d. cos B = 0.64

A B

Ex.4: Find the to the nearest degree. O

4

L 2.5 F

m L

Ex.5: Solve the right triangle. Round decimal answers to the nearest tenth.

• Solve the right triangle. Round decimal answers to the nearest tenth.

Ex.6: Ex.7: X

42o

A

50

3 5.8

Z Y B C

Ex.8: Solve a right triangle that has a 40o angle and a 20 inch hypotenuse.

Ex.9: Suppose your school is building a raked stage. The stage will be 30 feet long from front to back with a total rise of 2 feet. A rake (angle of elevation) of 5o or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested?