Question

Tutorial Exercise For the triangle shown in the figure below what are each of the following? (Let y 36.0 m and r-39.0 m. Assume the triangle is a right triangle.) (a) the length of the unknown side (x) (b) the tangent of θ (c) the sin of φ Step 1 We can find the length of the unknown side, labeled x in the figure, by applying the Pythagorean theorem. 2-x2+y2 Solving for x, we have and we have Submit Skip (you cannot come back)

Answer 1

(a) By pythagorean theorem -

r^2 = x^2 + y^2

=> x^2 = r^2 - y^2

=> x = sqrt[r^2 - y^2]

Put the values -

x = sqrt[39.0^2 - 36.0^2] = sqrt[225] = 15.0 m

(b) tangent of $\Theta$ = tan$\Theta$ = y/x = 36.0/15.0 = 2.4

(c) sin of $\phi$ = sin$\phi$ = x/r = 15.0 / 39.0 = 0.385