Question

find gh.
triangle image with right angle at h, hypotenuse gi = 7.3, angle at i is 33°
write your answer as an integer or as a decimal rounded to the nearest tenth.
gh = \boxed{}

Explanation:

Step1: Recall the cosine function in a right - triangle

In a right - triangle $\triangle HIG$ with $\angle H = 90^{\circ}$, the cosine of an angle $\theta$ is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 33^{\circ}$, the adjacent side to $\angle I$ is $GH$, and the hypotenuse is $IG = 7.3$. So, $\cos(33^{\circ})=\frac{GH}{IG}$.

Step2: Solve for $GH$

Since $IG = 7.3$ and $\cos(33^{\circ})\approx0.8387$ (using a calculator in degree mode), and from $\cos(33^{\circ})=\frac{GH}{7.3}$, we can rewrite the formula as $GH=7.3\times\cos(33^{\circ})$.
Substitute the value of $\cos(33^{\circ})$: $GH = 7.3\times0.8387$.
Calculate $7.3\times0.8387=(7 + 0.3)\times0.8387=7\times0.8387+0.3\times0.8387=5.8709+0.25161 = 6.12251\approx6.1$.

Answer:

$6.1$