Question

Solving Right triangles where the two legs are given. Equation no. 1: Triangle ABC is right angled at C. if a = 18.5 and b = 14.2: Find ZA, ZB and c

Answer 1

To find:

The angle A and angle B and side c.

Solution:

Given a = 18.5 and b = 14.

if we take tangent of angle A, then

`\begin{gathered} \tan A=(a)/(b) \\ \Rightarrow\tan A=(18.5)/(14.2) \\ \Rightarrow A=\tan^(-1)((18.5)/(14.2)) \\ \Rightarrow A=52.49\text{ degrees} \end{gathered}`

It is known that the sum of all three angles is 180 degrees. So,

`\begin{gathered} A+B+C=180 \\ 52.49+B+90=180 \\ B=37.51\text{ degrees} \end{gathered}`

Now, we use Pythagoras theorem to find the value of c:

`\begin{gathered} c^2=a^2+b^2 \\ c^2=14.2^2+18.5^2 \\ c^2=201.64+342.25 \\ c^2=543.89 \\ c=23.32 \end{gathered}`

Thus, angle A = 52.49 degrees, angle B = 37.51 degrees and c = 23.32.