Question

chapter 8 review score: 100/150 answered: 10/15 question 11 note: triangle may not be drawn to scale. suppose a = 4 and c = 8. find: b = a = degrees b = degrees give all answers to at least one decimal place. give angles in degrees question help: post to forum submit question

Explanation:

Step1: Find side b using Pythagorean theorem

Since it's a right - triangle, by the Pythagorean theorem $b=\sqrt{c^{2}-a^{2}}$. Given $a = 4$ and $c = 8$, we have $b=\sqrt{8^{2}-4^{2}}=\sqrt{64 - 16}=\sqrt{48}=4\sqrt{3}\approx6.9$.

Step2: Find angle A using sine function

$\sin(A)=\frac{a}{c}$. Substituting $a = 4$ and $c = 8$, we get $\sin(A)=\frac{4}{8}=0.5$. Then $A=\sin^{-1}(0.5)=30.0^{\circ}$.

Step3: Find angle B

Since the sum of angles in a triangle is $180^{\circ}$ and one angle is $90^{\circ}$, $B = 180^{\circ}-90^{\circ}-A$. Substituting $A = 30^{\circ}$, we get $B=60.0^{\circ}$.

Answer:

$b\approx6.9$
$A = 30.0$
$B = 60.0$