# Math Help - Trig

1. ## Trig

Stuck on this one...

The perimeter of a parallelogram is 44cm and the length of the shorter diagonal is 14cm. Find the lengths of the sides, given that they contain an angle of 60 degrees.

And this...

THe angles of elevation of the top of a tower from the top of a building 100m high are 50 and 75 respectively. FInd the height of the tower.

I drew diagrams but it still wont work out!

2. Originally Posted by classicstrings
Stuck on this one...

The perimeter of a parallelogram is 44cm and the length of the shorter diagonal is 14cm. Find the lengths of the sides, given that they contain an angle of 60 degrees.
And this...

THe angles of elevation of the top of a tower from the top of a building 100m high are 50 and 75 respectively. FInd the height of the tower.

I drew diagrams but it still wont work out!
Hello,

I've attached a drawing.
1. two neighbored sides form a triangle together with the short diagonal.
To calculate the sides you have to use the Cosine Rule:
$14^2=x^2+(22-x)^2-2 \cdot x \cdot (22-x) \cdot \cos(60^{\circ})$

with $\cos(60\circ})=\frac{1}{2}$ you'llget a quadratic equation:
$3x^2-66x+288=0$ and the solutions for x= 16 or x= 6.

Next problem will follow. Now I'm in a hurry.

Greetings

EB

3. Originally Posted by classicstrings
Stuck on this one...

...
THe angles of elevation of the top of a tower from the top of a building 100m high are 50 and 75 respectively. FInd the height of the tower.

I drew diagrams but it still wont work out!
Hello,

I'm awfully sorry, but are you sure that this is the complete problem? There must be at least one value (or another point) to calculate the height.