Question

solve for x. round to the nearest tenth of a degree, if necessary.
right triangle hij with right angle at i, hi = 2.8, ij = 4.2, angle at h is x degrees
answer attempt 1 out of 2
x = blank °
submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( HIJ \), for angle \( x \) at \( H \), the opposite side to \( x \) is \( IJ = 4.2 \) and the adjacent side is \( HI = 2.8 \). So we use the tangent function: \( \tan(x)=\frac{\text{opposite}}{\text{adjacent}}=\frac{IJ}{HI} \).

Step2: Substitute values

Substitute \( IJ = 4.2 \) and \( HI = 2.8 \) into the tangent formula: \( \tan(x)=\frac{4.2}{2.8} \). Simplify \( \frac{4.2}{2.8}=1.5 \).

Step3: Solve for \( x \)

Take the arctangent (inverse tangent) of both sides: \( x = \arctan(1.5) \). Using a calculator, \( \arctan(1.5)\approx56.3^\circ \) (rounded to the nearest tenth).

Answer:

\( 56.3 \)