Question

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

Answer 1

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:

$\tan 36^o=\frac{85}{x}$

Solving for x:

$x=\frac{85}{\tan 36^o}$

Calculating:

$x=\frac{85}{0.7265}=116.99$

Now we use the other triangle at the right:

$\tan 50^o=\frac{85}{y}$

Solving for y:

$y=\frac{85}{\tan 50^o}$

Calculating:

$y=\frac{85}{1.1918}=71.32$

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