1. 8-3 Solving Right Triangles
Geometry

2. To solve a right triangle
To solve a right triangle means to determine the measures of all six parts;
1 right angle
2 acute angles
1 hypotenuse
2 legs

3. If you know the sine, cosine and the tangent of an acute angle,
then you can use a calc. to find the measure of the angle.
In general, for an acute angle A:
if sin A = x, then
if cos A = y, then
If tan A = z, then

4. Ex. 1 Identifying angles from Trig ratios
Use the trigonometric ratio cos A =
to determine which angle of the triangle is
5 ft
1.4 ft
4.8 ft

5. Inverse Trig Functions
If sin A = x, then
If cos A = x, then
If tan A = x, then

6. Ex. 2
Use your calculator to find each angle measure to the nearest degree.
A.)
B.)
C.)

7. Ex. 3
Find the unknown measures. Round lengths to the nearest hundredth & angle measures to the nearest degree. S 5 R 5.7 T

8. Ex. 4
The coordinates of the vertices of are P(-3,3), Q(2,3) & R(-3,-4). Find the side lengths to the nearest hundredth & the angle measures to the nearest degree.

9. Ex. 5
A highway sign warns that a section of road ahead has a 7% grade. To the nearest degree, what angle does the road make with a horizontal line?

10. Assignment

11. Ex. 3
During a flight, a hot air balloon is observed by two persons standing at points A and B as illustrated in the diagram. The angle of elevation of point A is Point A is 1.8 miles from the balloon as measured along the ground.
a.) What is the height h of the balloon?

12. Ex. 3 (Cont’d)
During a flight, a hot air balloon is observed by two persons standing at points A and B as illustrated in the diagram. The angle of elevation of point A is Point A is 1.8 miles from the balloon as measured along the ground.
b.) Point B is 2.8 miles from point A. Find the angle of elevation of point B.