Question

solve for x. round to the nearest tenth of a degree, if necessary.
(image of a right triangle with right angle at b, ab = 15, bc = 25, angle at c is x°)

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the side opposite to angle \(x\) is \(AB = 15\) and the side adjacent to angle \(x\) is \(BC=25\). So, \(\tan x=\frac{15}{25}\).

Step2: Simplify the fraction and find the arctangent

Simplify \(\frac{15}{25}=\frac{3}{5} = 0.6\). Then, \(x=\arctan(0.6)\). Using a calculator, \(x=\arctan(0.6)\approx31.0^{\circ}\)

Answer:

\(31.0^{\circ}\)