Question

Find the value of each variable. Give exact answers.

Answer 1

Answer:

See below

Step-by-step explanation:

Finding a:

$\displaystyle sin (\theta) = \frac{opposite }{hypotenuse}$

Where θ = 45° , opposite = a, hyp = 4√2

$\displaystyle sin (45)=\frac{a}{4\sqrt{2} } \\\\\frac{1}{\sqrt{2} } = \frac{a}{4\sqrt{2} } \\\\1 = \frac{a}{4} \\\\\boxed{a = 4}$

Finding c:

$\displaystyle tan (\theta) = \frac{opposite }{adjacent}$

Where θ = 45°, opposite = 4, adjacent = c

tan 45 = 4 / c

1 = 4 / c

Multiply both sides by c

c = 4

Finding b:

$\displaystyle sin(\theta) = \frac{opposite}{hypotenuse}$

Where θ = 30°, opposite = a(4), hypotenuse = b

sin 30 = 4 / b

$\displaystyle \frac{1}{2} = \frac{4}{b}$

Cross Multiply

1 * b = 4 * 2

b = 8

Finding d:

$\displaystyle tan (\theta) = \frac{opposite }{adjacent}$

Where θ = 30°, opposite = a(4) , adjacent = d

tan 30 = 4 / d

$\displaystyle \frac{1}{\sqrt{3} } = \frac{4}{d}$

Cross Multiplying

1 * d = 4√3

$\boxed{d = 4\sqrt{3}}$

$\rule[225]{225}{2}$

Hope this helped!

~AH1807