In this civil engineering article, you will get some useful tips to determine the height of an object with angle and distance. The article is very useful for surveyors.

The following formulas are used for calculation purpose:-

Sinθ = P/H (P stands for perpendicular and h stands for hypotenuse)

Cosθ = B/H (B stands for base)

Tanθ = P/B

It should be remembered that the opposite of the angle (in a triangle) is always perpendicular.

Here, the value of θ is taken as 45 degree and the value of base is taken as 10 meter

Now, Tanθ = P/B

Now, after putting the values, we get the following result:-

tan45⁰ = P/B = P/10

As we know the value of tan45⁰ = 1

So, 1 = P/10 or P = 10

So, P = 10m

Now, Sinθ = P/H

After putting the value, we get the following result:-

Sin45⁰ = 10/H (as height is taken as 10m)

So, 0.707 = 10/H or H = 10/0.707 = 14.14m (value of Sin45⁰ = 0.707)

Now, Cosθ = B/H

So, Cos45⁰ = 10/H (as the value of base = 10)

So, 0.707 = 10/H or H = 10/0.707 = 14.14m