help with question II

[yfelix45]

Hello again,

This question i have attempted before and I got confused about how i should approach solving it.

A patio umbrella is being designed in the shape of a square based pyramid. The lengths of the sides are all 2m. The height AD of the umbrella is 0.5m. Find the lengths of the sides of the triangular pieces(AB and AC) and the measure of angle BAC.

height = 0.5m

side AB = 2m

side AC = 2m

angle BAC = x


What i did:

angle B and C are isoceles trtiangles

tan x = 0.5/2
tanx = 0.25
x = tan^-1 0.25
x = 14.0

b^2 =(2)^2 + (2)^2 -2(2)(2)cos14
b^2 = 0.24
b=sqrt 0.24
b = 0.48
b= 0.5

Is what I have done right? How would you solve this question differently?
thanks
yfelix45

 

[Freeman]

The base is a square, BDC is a right isoscels triangle. AD is perpendicular to the base.
AD=0.5, BD=CD=BCcos45°=2/sqrt2=sqrt2. AB=AC=sqrt(0.5^2+2)=1.5.
cos∠BAC=(AB^2+AC^2-BC^2)/(2AB.AC)=(1.5^2+1.5^2-2^2)/(2*1.5*1.5)=1/9, ∠BAC=83.62°.

 

[yfelix45]

Thanks

hello freeman

Thank you for your help with my question

yfelix45