Question

A pole 7 meters long is placed against a wall at an angle of 45 degrees, what is the height of the wall

Answer 1

since the angle is 45º, you have an isosceles right-angled triangle
so 7 is the hypotenuse and each of the other two sides can be called x

x^2 + x^2 = 7^2
2x^2 = 49
x^2 = 24.5
x = √24.5 = approx. 4.95 m

OR

sin 45º = height of wall/7
height of wall = 7sin45º
= 7(.7071067)
= appr. 4.95 m

Answer 2

If the top of the pole (of length L) rests on the top of the wall, the wall height H is such that
sin 45 = H/L = (sqrt2)/2
Solve for H

Answer 3

Use a trig function that states
opposite/hypotenuse.

Of course, this would be the sine function.

sin(45degrees) = h/7meters

Let h = height of building

sin45 = h/7

sin45 times 7 = h

4.949747468 = h

Round 4.949747468 to the nearest tenths becomes 4.95 meters.

The height of the building is about
4.95 meters in height.