Question

If segment FD = 30 units and segment FE = 55 units, what is the value of a? Round the solution to the nearest hundredth. triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees 22.62 28.44 41.41 61.39

Answer 1

Answer:

$61.39^\circ$ is the correct answer.

Step-by-step explanation:

We are given a right angled triangle $\triangle$DEF with the following dimensions:

FD = 30 units

FE = 55 units

$\angle D = a^\circ\\\angle E = b^\circ$

We have to find the value, a = ?

Please refer the attached image for the given triangle.

We can use trigonometric identities to find the value of a.

First of all, if we look at angle a, we can see that, we are given with the perpendicular (side FE) and base (side DF).

It means we can choose tangent among sine, cosine and tangent because perpendicular and base are used the identity. It is given as follows:

$tan\theta =\dfrac{Perpendicular}{Base}$

$tana =\dfrac{FE}{DF}\\tana =\dfrac{55}{30}\\tana =1.83\\a = tan^{-1} (1.83)\\a = 61.39^\circ$

So, $a=61.39^\circ$ is the correct answer.