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Give both an exact solution and an approximate solution to two decimal places for the following. Given: right AABC with mzC = 90° and mzBAC = 60° point D on BC AD bisects zBAC and AC = 5/3 Find: BD

Give both an exact solution and an approximate solution to two decimal places for the following. Given: right AABC with mzC = 90° and mzBAC = 60° point D on BC AD bisects zBAC and AC = 5/3 Find: BD

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 33E
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Give both an exact solution and an approximate solution to two decimal places for the following. Given: right AABC with mzC = 90° and mzBAC = 60° point D on BC AD bisects 2BAC and AC = 5V3 Find: BD C.O exact BD = approximate BD =
Transcribed Image Text:Give both an exact solution and an approximate solution to two decimal places for the following. Given: right AABC with mzC = 90° and mzBAC = 60° point D on BC AD bisects 2BAC and AC = 5V3 Find: BD C.O exact BD = approximate BD =
Expert Solution
Step 1

Given Data:

The measure of ∠C is: m∠C=90°

The measure of ∠BAC is: m∠BAC=60°

The length of side AC is: AC=53

The segment AD bisects ∠BAC.

The measure of ∠DAC is,

m∠DAC=m∠BAC2

Substitute the values in the above equation.

m∠DAC=60°2=30°

Step 2

For exact BD,

The length of CD is,

CD=ACtanm∠DAC

Substitute the values in the above equation.

CD=53tan30°=5313=51=5

The length of BC is,

BC=ACtanm∠BAC

Substitute the values in the above equation.

BC=53tan60°=533=53=15

The exact value of BD is,

BD=BC-CD

Substitute the values in the above equation.

BD=15-5=10

Thus, the exact value of BD is 10.

 

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