Chapter 10 - NCPN

Lesson 10.1 Right Triangle Trigonometry
Objectives
Find lengths in triangles
using trigonometric
relationships.
From where Horacio stands at a distance of 38 feet from the base of
the school building, the angle to the top of the school is 40°. What is
the height of the school building
Activity
Finding Right Triangle Ratios
Use a protractor and a straightedge to
draw three right triangles on a sheet
of paper. Each triangle should have an
acute angle that measures 50°. Label
this angle a in each triangle. Make
the hypotenuses of the three similar
triangles 5, 8, and 10 centimeters.
1 Measure the lengths of the legs of each right triangle to the
nearest tenth. Small: 3.8 cm, 3.2 cm; Medium: 6.1 cm, 5.1 cm;
Large: 7.7 cm, 6.4 cm
2 What is the ratio of the length of the leg opposite ∠a to
the length of the hypotenuse in each triangle Round to the
nearest tenth. 0.8 for each triangle
3 What is the ratio of the length of the leg adjacent to ∠a to
the length of the hypotenuse in each triangle Round to the
nearest tenth. 0.6 for each triangle
4 What is the ratio of the length of the leg opposite ∠a to the
length of the leg adjacent to ∠a in each triangle Round to
the nearest tenth. 1.2 for each triangle
5 Make a conjecture about these ratios for all right triangles
that have an acute angle of 50°. The ratios are the same for any
right triangle with an acute angle of 50°.
436 Chapter 10 Trigonometric Functions and Identities