Question

The picture shows a triangular island. Which expression shows the value of z?

Answer 1

x sin 50*
y/cos 50*
x/cos 50*
y/sin 50*

Answer 2

sorry, I don't get it:( What is the answer?

Answer 3

@jdoe0001

Answer 4

use your SOH CAH TOA \(sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}

\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}\)

the tangent, in this case,doesn't have a hypotenuse, so, it won't work on this one

the cosine and sine do, so.... solve either for hypotenuse

Answer 5

\(\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\ \quad \\
\begin{cases}
\theta=50\\
adjacent= y\\
opposite=x
\end{cases}\implies sin(50)=\cfrac{x}{z}\qquad or\qquad cos(50)=\cfrac{y}{z}
\\ \quad \\
\textit{solve either for "z"}\)

Answer 6

just do a quick cross-multiplication, on either, to get "z"