How do I find the base of this triangle? 36degrees50 degrees94 degrees Height is 85

Question

asked May 22, 2023 103k views

1 Answer

Darielle · Answer 1 · 2023-05-28T07:10:12+0000

Find the base of the given triangle

We need to add two variables to find the base. They can be seen in the image below:

The length of the base is then calculated as B = x + y

Let's focus on the triangle at the left. We are given its height h=85 and the base angle of 36°.

Recalling the tangent of an angle relates the opposite side of the triangle to its adjacent side as follows:

$\tan 36^o=(85)/(x)$

Solving for x:

$x=(85)/(\tan 36^o)$

Calculating:

Now we use the other triangle at the right:

$\tan 50^o=(85)/(y)$

Solving for y:

$y=(85)/(\tan 50^o)$

Calculating:

Finally, the length of the base is:

B = x + y = 116.99 + 71.32 = 188.32

The length of the base is 188.32 units