Kirsten is sitting in a tree house reading and notices her dog Penny starting to dig a hole 40 meters away from the base of the
tree. Penny, the dog, looks up at Kirsten in the tree house at an angle of elevation of 30°, then continues to dig. How high is the
tree house?

The tree house is 23.09 meters high

Step-by-step explanation:

Kirsten is sitting in a tree house reading and notices her dog Penny starting to dig a hole 40 meters away from the base of the

tree. Penny, the dog, looks up at Kirsten in the tree house at an angle of elevation of 30°, then continues to dig. How high is the

tree house?

To find the height of the tree house, we will follow the steps below;

we can use the trigonometric ratios to solve the problem

SOH CAH TOA

sin Ф = opposite / hypotenuse

cosФ = adjacent / hypotenuse

tan Ф = opposite / adjacent

From the diagram below,

angle Ф = 30°

adjacent = 40 meters

opposite = h   where h is the height of the tree house

From the parameters we have, the best trigonometric ratio to use is tan

tan Ф = opposite / adjacent

tan 30° =

cross-multiply

h = 40 tan 30°

h ≈ 23.09 meters

Therefore, the tree house is 23.09 meters high