A right-angled triangle has one of its angles to be 90 degrees
The unknown measurements are:
[tex]BC = 10.1[/tex]
[tex]AB = 15.7[/tex]
[tex]\angle B = 50[/tex]
From the question, we have:
[tex]\angle A = 40^o[/tex]
[tex]\angle C = 90^o[/tex]
[tex]AC =12[/tex]
See attachment for [tex]\triangle ABC[/tex]
First, we calculate the measure of B
[tex]\angle A + \angle B + \angle C = 180[/tex]
This gives
[tex]40 + \angle B + 90 = 180[/tex]
Collect like terms
[tex]\angle B = 180 - 40 - 90[/tex]
[tex]\angle B = 50[/tex]
Side length BC is calculated using the following tangent ratio
[tex]\tan(A) = \frac{BC}{AC}[/tex]
Make BC the subject
[tex]BC = AC \times \tan(A)[/tex]
So, we have:
[tex]BC = 12 \times \tan(40)[/tex]
[tex]BC = 10.1[/tex]
Side length AB is calculated by Pythagoras theorem.
[tex]AB^2 = AC^2 + BC^2[/tex]
So, we have:
[tex]AB^2 = 12^2 + 10.1^2[/tex]
[tex]AB^2 = 246.01[/tex]
Take positive square roots of both sides
[tex]AB = 15.7[/tex]
Hence, the unknown measurements are:
[tex]BC = 10.1[/tex]
[tex]AB = 15.7[/tex]
[tex]\angle B = 50[/tex]
Read more about right-angled triangles at:
https://brainly.com/question/3770177
