Question

chapter 6 quiz
170 points possible answered: 13/17
question 14
note: triangle may not be drawn to scale.
suppose a = 4 and b = 3.
find:
c=
a=
degrees
b=
degrees
give all answers to at least one decimal place. give angles in degrees
add work

next question

Explanation:

Step1: Find the length of side \(c\)

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\). Given \(a = 4\) and \(b=3\), then \(c=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\).

Step2: Find the measure of angle \(A\)

Use the trigonometric ratio \(\tan A=\frac{a}{b}\). So \(\tan A=\frac{4}{3}\), and \(A=\arctan(\frac{4}{3})\approx53.1^{\circ}\) (using a calculator).

Step3: Find the measure of angle \(B\)

Since the sum of angles in a triangle is \(180^{\circ}\) and it is a right - triangle (\(90^{\circ}\) angle), \(B = 90^{\circ}-A\). So \(B=90^{\circ}- 53.1^{\circ}=36.9^{\circ}\)

Answer:

\(c = 5\), \(A\approx53.1\) degrees, \(B\approx36.9\) degrees