Question

i need to find the measure of angle b in a right triangle... the base is 4. they hypotenuse is 9 and angle c is the right angle.... also angle b is the top angle in the triangle

Answer 1

One way to solve this question is through trigonometry. :)

If you've learnt trigonometry, here are the basic formulas:
SOH CAH TOA (These formulas only apply for right-angled triangles)

Sin(angle) = (Side that is Opposite of angle)/(Hypotenuse)

Cos(angle) = (Side that is Adjacent of angle)/(Hypotenuse)

Tan(angle) = (Side that is Opposite of angle)/(Side that is Adjacent of angle)

In this case, we should use sine of b (the angle at the top of triangle as indicated in your question), where the opposite side is the base (I.e. 4 indicated in your question) and the hypotenuse is 9.

sin(b) = 4/9
{Make angle b the subject of the equation}
$b = {sin}^{ - 1} ( \frac{4}{9} )$
{Type this into the calculator}
Angle b = 26.4° (rounded off to 1 decimal place)

Hope this helps! :)