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=(85)/(x)`

Solving for x:

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

Calculating:

`x=(85)/(0.7265)=116.99`

Now we use the other triangle at the right:

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

Solving for y:

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

Calculating:

`y=(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