Ch. 1 - Trigonometric Functions

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 1 - Trigonometric Functions

Problem 23

Chapter 2, Problem 23

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°

Verified step by step guidance

Recall that the sum of the interior angles of any triangle is always 180 degrees. This is a fundamental property of triangles.

Identify the given angles: 37° and 52°.

Set up an equation to find the third angle, which we'll call \( x \):

\[ 37 + 52 + x = 180 \]

Combine the known angles on the left side:

\[ 89 + x = 180 \]

Solve for \( x \) by subtracting 89 from both sides:

\[ x = 180 - 89 \]

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Triangle Angle Sum Property

The sum of the interior angles of any triangle is always 180 degrees. This fundamental property allows us to find the measure of the third angle when the other two angles are known by subtracting their sum from 180°.

Basic Arithmetic Operations

To find the unknown angle, you need to perform simple addition and subtraction. First, add the two given angles, then subtract their sum from 180° to get the third angle's measure.

Angle Measurement Units

Angles are measured in degrees (°), a unit that divides a full rotation into 360 parts. Understanding this unit is essential for interpreting and calculating angle measures correctly.

Recommended video:

5:31

Reference Angles on the Unit Circle

Related Practice

Textbook Question

In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.

views

Textbook Question

Find the measure of each marked angle. See Example 2.

Textbook Question

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.

sin θ , given that csc θ = 1.25

Textbook Question

Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30-ft tree be at the same time and place?

Textbook Question

Find the measure of each marked angle. See Example 2.

Textbook Question

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 50° 40' 50"

views