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

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

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 =(base)/(hypotenuse)}}`

Put on the respective values ,

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