Question

Find the exact value of the given angle. Simply all radicals and rationalize all denominators.

Answer 1

4√33/33

Explanation:

Solution,

Here,

sinθ=4/7

p/h=4/7

b=?

Now using Pythagoras theorem,

`\hookrightarrow h^(2) =p^(2) +b^(2) \\\\\hookrightarrow (7)^(2) =(4)^(2) +b^(2)\\\\\hookrightarrow 49-16=b^(2) \\\\\hookrightarrow b=√(33)`

Again,

tanθ=p/b

`tan\theta=(4)/(√(33) ) \\\\tan\theta=(4)/(√(33) ) * (√(33) )/(√(33) ) \\\\tan\theta=(4√(33) )/(33)`

Answer 2

According to the question ,

Sin θ = 4/7

We know that , Sin θ = Perpendicular/Hypotenuse

So , by Pythagoras theorem

• Perpendicular = 4 units
• Hypotenuse = 7 units
• Base = let it be x

Hypotenuse² = Perpendicular ² + Base ²

7² = 4² + x²

49-16 = x²

√33 = x

5.7 = x

So , the base is 5.7 units (approx)

Tan θ = Perpendicular/base

Tan θ = 4/5.7