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 Penny the dog, looks up at Kirsten in the tree house at an angle of elevation of 30 degrees , then continues high is the tree house?

23.09 m  

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Tan α = opposite side / adjacent side

Where α is the angle of elevation that the dog is looking up, the opposite side (x) is the height of the tree house, and the adjacent side is the distance between the dog and the tree house base.  

Replacing with the values given:  

Tan 30 = x/ 40

Solving for x  

tan30 (40) =x  

x= 23.09 m  

Feel free to ask for more if needed or if you did not understand something.  

take it another

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.