Question

find the measure of x. 78° 26 x x =? round to the nearest hundredth

Explanation:

Step1: Identify trig - function

In a right - triangle, we use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 78^{\circ}$, the hypotenuse is 26, and the opposite side to the angle $\theta$ is $x$.
So, $\sin(78^{\circ})=\frac{x}{26}$.

Step2: Solve for $x$

Multiply both sides of the equation by 26: $x = 26\times\sin(78^{\circ})$.
We know that $\sin(78^{\circ})\approx0.9781$.
Then $x = 26\times0.9781$.
$x\approx25.43$.

Answer:

$25.43$