Question

Using trigonometric ratios find the remaining side lengths and angle measurements to 2 decimal places each:

(a) α = 35°, β = 90°, a = 30

(b) α = 90°, b = 7, c = 6

(c) a = 33, b = 56, c = 65

Answer 1

The first two triangles are clearly right-angled.
Is the third one ?
is 65^2 = 33^2 + 56^2 ??, YES

So make sketches of each one.
for a) I labeled by triangle ABC, where a = 30
angle A = 90, and angle B = 30°
sin35° = 30/b
bsin35 = 30
b = 30/sin35 = appr 52.30

tan35 = 30/c
c = 30/tan35 = appr 42.84

(after I found b, I could have used Pythagoras to find c
c^2 + 30^2 = 52.3^2
c^2 = 1835.29
c = 42.84, confirming my answer above )

So the others the same way

for the last one, obviously the 90° angle is opposite the largest side.
use tanØ to find one of the 2 missing angles, the third one is then obvious.