Download Section 2.4: Solving Right Triangles

Chapter 2
Section 2.4
Section 2.4: Solving Right Triangles
I.
Significant Digits

A significant digit is a digit obtained by actual measurement.

The significant digits in the following numbers are identified in bold:
408
21.5
18.00
6.700
0.0025
0.09810
7300
Rule of Thumb
Your answer is no more accurate than the
least accurate number in your calculation.

II.
To determine the number of significant digits for answers in applications of angle measure,
use the following table:
Solving Triangles

To solve a triangle means to find the measures of all the angles and sides of the triangle.

When solving triangles, a labeled sketch is an important
aid. Use a to represent the length of the side opposite
angle A, b for the length of the side opposite angle B,
and so on. In a right triangle, the letter c is reserved for
the hypotenuse.
Chapter 2
Section 2.4
Example 1 (Solving a Right Triangle Given an Angle and a Side): Solve right triangle ABC, if
B = 28°40′ and a = 25.3 cm.
Side-Notes:

We could have found the measure of angle A first or the values of the unknown sides first. A
right triangle can usually be solved in several ways, each producing the correct answer.

To maintain accuracy, always use given information as much as possible, and avoid
rounding off in intermediate steps.
Chapter 2
Section 2.4
Example 2 (Solving a Right Triangle Given Two Sides): Solve right triangle ABC, if a = 44.25 cm
and b = 55.87 cm.
III.
Angles of Elevation or Depression

The angle of elevation from point X to
point Y (above X) is the acute angle
formed by ray XY and a horizontal ray
with endpoint at X.
CAUTION
Be careful when interpreting the angle of
depression.
Both the angle of elevation and the angle
of depression are measured between the
line of sight and a horizontal line.

The angle of depression from point X to
point Y (below X) is the acute angle
formed by ray XY and a horizontal ray
with endpoint X.
Chapter 2

Section 2.4
George Polya (1887 – 1985), How to Solve It.
Solving an Applied Trigonometry
Problem
STEP 1:
Draw a sketch, and label it with the given information. Label the
quantity to be found with a variable.
STEP 2:
Use the sketch to write an equation relating the given quantities to the
variable.
STEP 3:
Solve the equation, and check that your answer makes sense.
Example 3 (Finding a Length Given the Angle of Elevation): The angle of depression from the top
of a tree to a point on the ground 15.5 m from the base of the tree is 60.4°. Find the height of the tree.
Practice: Find the angle of depression from the top of a 97-ft building to the base of a building across
the street located 42 ft away.