can someone help with this question?
I tried roughly sketching it out first. I've attached the bird's eye view and side views of the scenario to help.
If you follow my sketch:
Let height of tower = x metres
Let horizontal length from tower to B = y metres
As angle of elevation to top of tower from A is 45 degrees, we know horizontal distance from tower to A is also x metres (equal to height of tower).
As angle of elevation to top of tower from B is 26 degrees, we can use SOHCAHTOA to calculate that:
tan(26) = x/y
Transpose to find y in terms of x:
y = x/tan(26)
Use cosine rule on triangle (bird's eye view) to determine value of x:
y^2 = x^2 + 100^2 – 2(x)(100)cos(60)
(x/tan(26))^2 = x^2 + 100^2 – 2(x)(100)cos(60)
Solve for x using CAS:
x = 42.40, -73.61
x must be 42.4 metres as x > 0
Thus height of tower being x, is 42.4 metres tall.
Hope I helped!
P.S. Sorry for the dodgy drawing!