Question

1. find the value of x. show all steps.

not drawn to scale
a. 11.4
b. 8.1
c. 7.6
d. 6.5
find the value of x. round to the nearest degree.

1. not drawn to scale

a. 62
b. 25.5
c. 28
d. 25

1. not drawn to scale

a. 41
b. 36
c. 46
d. 44
a. find the value of each trigonometric ratio.
tan z sin a cos

Explanation:

Step1: Identify the trigonometric ratio

We use the cosine ratio for a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 36^{\circ}\), the hypotenuse \(h = 10\), and the adjacent side is \(x\).
So, \(\cos36^{\circ}=\frac{x}{10}\).

Step2: Solve for \(x\)

We know that \(\cos36^{\circ}\approx0.8090\).
From \(x = 10\times\cos36^{\circ}\), substituting the value of \(\cos36^{\circ}\), we get \(x\approx10\times0.8090 = 8.09\approx8.1\).

Step1: Identify the trigonometric ratio

We use the sine ratio for a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to \(x^{\circ}\) is \(7\) and the hypotenuse is \(15\). So, \(\sin x=\frac{7}{15}\).

Step2: Solve for \(x\)

\(x=\sin^{- 1}(\frac{7}{15})\). Using a calculator, \(\sin^{-1}(\frac{7}{15})\approx27.8^{\circ}\approx28^{\circ}\).

Step1: Identify the trigonometric ratio

We use the cosine ratio for a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to \(x^{\circ}\) is \(15\) and the hypotenuse is \(21\). So, \(\cos x=\frac{15}{21}=\frac{5}{7}\).

Step2: Solve for \(x\)

\(x = \cos^{-1}(\frac{5}{7})\). Using a calculator, \(\cos^{-1}(\frac{5}{7})\approx44.4^{\circ}\approx44^{\circ}\).

Answer:

b. 8.1