Question

question 10 of 10
what is the length x of the side of the triangle below? (hint: use the cosine
function.)
a. 4.7
b. 4.2
c. 9.1
d. 9.7

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 25^{\circ}\), the hypotenuse \(= 10\), and the adjacent side is \(x\). So, \(\cos(25^{\circ})=\frac{x}{10}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(25^{\circ})=\frac{x}{10}\) by \(10\). We know that \(\cos(25^{\circ})\approx0.9063\). Then \(x = 10\times\cos(25^{\circ})\). Substitute \(\cos(25^{\circ})\approx0.9063\) into the equation, \(x\approx10\times0.9063 = 9.063\approx9.1\).

Answer:

C. 9.1