Question

as the connected complexity of mathematical concepts evolve, your mathematical knowledge evolves as well. previous knowledge provides the necessary skills to acquire new learning. if necessary, review the solving right triangles skill builder, to strengthen your understanding of this topic. calculate the value of x in each diagram below. (diagrams not to scale.) homework help a. 10 77° x

Explanation:

Step1: Use sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 77^{\circ}$, the opposite side to the angle $\theta$ has length $10$, and the hypotenuse has length $x$. So, $\sin77^{\circ}=\frac{10}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{10}{\sin77^{\circ}}$. Since $\sin77^{\circ}\approx0.9744$, then $x=\frac{10}{0.9744}\approx10.26$.

Answer:

$x\approx10.26$