A rope with a length of 4 meters is tied from a stake in the ground to the top of a tent. It forms a 20 degree angle with the ground. How tall is the tent?

Question

asked Aug 23, 2021 118k views

1 Answer

Kamidu Punchihewa · Answer 1 · 2021-08-27T07:54:38+0000

Answer:
$1.36\ m$

Explanation:

Draw a right triangle where "x" is the height in meters of the tent (Observe the picture attached).

You need to use the following Trigonometric Identity:

$sin\alpha =(opposite)/(hypotenuse)$

In this case, you can identify that:

$\alpha=20\°\\\\opposite=x\\\\hypotenuse=4$

Now you must substitute these values into
$sin\alpha =(opposite)/(hypotenuse)$ . Then:

$sin(20\°) =(x)/(4)$

Finally you must solve for "x" in order to find its value.

This is:

$4*sin(20\°)=x\\\\x=1.36$