Question

Please help me I would really appreciate it

Answer 1

Cos = adjacent / hypotenuse

cos B = 4/5

B = cos^-1 (4/5)

B = 36.869897....

B = 36.87° (nearest hundredth)


Angle B = 36.87°.

Answer 2

Answer:

$\boxed{\textsf{ The measure of unknown angle is \textbf{ 37} ^{\circ} .}}$

Step-by-step explanation:

A right angled triangle is given to us with the sides 3 and 4 . We need to find the value of unknown angle that is $\sf \angle ABC$ .

So , here the measure of hypotenuse is 5 units .

$\sf \implies Hypotenuse = 5 \ units .$

And the measure of base is 4 units .

$\sf\implies Base = 4 \ units .$

Let us take the unknown angle be $\theta$ . That is let us take ,

$\sf \implies \angle ABC =\theta$

So here we can use the trigonometric ratios of cosine . The cosine can be expressed as a ratio of base and hypotenuse of a right angled triangle . Here ∆ABC . So , cosine is ,

$\qquad\boxed{\boxed{\sf cos\theta =\dfrac{base}{hypotenuse}}}$

Put on the respective values ,

$\sf\implies cos\theta =\dfrac{base}{hypotenuse}\\\\\sf\implies cos\theta =\dfrac{4}{5}\\\\\sf\implies \theta =cos^{-1}\bigg(\dfrac{4}{5}\bigg) \\\\\sf\implies \boxed{\pink{\sf \theta = 37^{o} . }}$