Question

Find the exact values of the indicated trigonometric functions. write fractions in lowest terms. right triangle acb is shown where segment ac is seven units, segment cb is twenty four units and segment ba is twenty five units. find sin b and tan

b.

Answer 1

sin b = length of opposite side / hypotenuse = ac /ba = 7/25
tan d = ac / bc = 7/24

Answer 2

In Right Δ ac b, Right angled at c,

Also, ac=7 units, b c=24 Units, and a b=25 units

Why Right angled at c, because

(ab)²=(ac)²+(b c)²

So,converse of Pythagoras theorem states that if in a triangle square of longest side is equal to sum of other two sides, then the triangle is right angled triangle.

As, ab is longest side that is Hypotenuse and , ac as altitude and c b as base are two shorter sides, so the triangle is right angled at c.

In Right Δ ac b,

`Sin b=\frac{\text{Perpendicular}}{\text{Hypotenuse}}=(7)/(25)\\\\ Tan b=\frac{\text{{Perpendicular}}}{\text{base}}=(7)/(24)`