The angle of elevation of the top of a tree from a point P on a horizontal ground is 30°.From another point Q 8 metres from the base of the tree,the angle of elevation of the angle of elevation of the top of the tree is 48°. a)Calculate to one decimal place the height of the tree. b)Calculate the distance btwn P and Q

7 answers

tan 48 = h/8

solve for h, the height
tan 30 = h/ (PQ+8)
solve for PQ

Plz explain am really having problem with this problem

h = 8 /tan 30 = 8 / .577 = 13.86

whoops, typo

h = 8 tan 48 = 8 * 1.11 = 8.88

PQ + 8 = 8.88/tan 30 = 8.88/.577 = 15.4

PQ = 15.4 - 8 = 7.39

Thanks alot

Did you know?

Did you know that the angle of elevation can be used to calculate the height of an object, such as a tree? In this particular scenario, if the angle of elevation of the top of a tree from a point P on horizontal ground is 30°, and from another point Q, located 8 meters from the base of the tree, the angle of elevation is 48°, we can determine the height of the tree. To calculate the height, we c an use trigonometry. By using the tangent function, we can find the height of the tree. In this case, tan(30°) = height/8 meters. Solving this equation, we find that the height of the tree is approximately 4.6 meters. Additionally, we can calculate the distance between points P and Q by using trigonometry as well. As we know the angle of elevation at point Q and the height of the tree, we can again use the tangent function. Therefore, tan(48°) = height/distance. Rearranging the equation, we find that the distance between points P and Q is approximately 4.8 meters. So, next time you are trying to measure the height of a tree or the distance between two points, remember that trigonometry can be a useful tool!