Question

Please help me tysm i dont understand

Answer 1

sinθ is equal to the division of the opposite side of the reference angle (θ) by the hypotenuse.

the cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse

tan30 = h/2

`tan30 = (1)/( √(3) )`

1/sqrt3 = h/2

`h = (2)/( √(3) )`

sin45 = 3/b

`sin45 = (1)/( √(2) )`

1/sqrt2 = 3/b

b/sqrt2 =3

`b = 3 √(2)`

Answer 2

h = 2
`√(3)`

b = 3
`√(2)`

Explanation:

to find 'h' we can use the ratio of sides in a 30-60-90° triangle which, respectively, is 1 :
`√(3)` : 2

so we can set up this proportion:

h/2 = 1/
`√(3)`

cross-multiply:

h = 2
`√(3)`

to find 'b' we can use the ratio of sides in a 45-45-90° triangle which, respectively, is 1 : 1 :
`√(2)`

we can set up this proportion:

3/b = 1/
`√(2)`

cross-multiply:

b = 3
`√(2)`