Answer:
option 4: Cosec ∠B equals 4 over 3
Step-by-step explanation:
Given :In Right triangle ABC
AB = 5
AC = 6
BC = 8.
Solution : we will use trigonometric ratios
.
Since we know that options are given for cot angle and cosec angle
So, we will consider trigonometric ratios of cosec angle and cot angle i.e.
cosec θ= Hypotenuse/Perpendicular
cotθ = Base/Perpendicular
Option 1 : cot angle B equals 6 over 5
Since cotθ = Base/Perpendicular
For ∠B base is AB and perpendicular is AC (refer the attached figure )
therefore , Cot ∠B = AB/AC
⇒Cot ∠B = 5/6
Thus Cot ∠B equals 5 over 6
while we are given cot angle B equals 6 over 5
Hence option 1 is wrong
Now, consider option 2 cosec angle C equals 3 over 4
cosec θ = Hypotenuse/Perpendicular
For ∠C perpendicular is AB and Hypotenuse is BC(refer the attached figure )
therefore , Cosec ∠C = BC/AB
⇒Cosec ∠C = 8/5
Thus Cosec ∠C equals 8 over 5
while we are given Cosec ∠C equals 3 over 4.
Hence option 2 is wrong.
Now, consider option 3 cot angle C equals 8 over 5
Since cotθ = Base/Perpendicular
For ∠C base is AC and perpendicular is AB (refer the attached figure )
therefore , Cot ∠C = AC/AB
⇒Cot ∠B = 6/5
Thus Cot ∠C equals 6 over 5
while we are given cot angle C equals 8 over 5
Hence option 3 is wrong.
Now, consider option 4 cosec angle B equals 4 over 3
cosec θ = Hypotenuse/Perpendicular
For∠B perpendicular is AC and Hypotenuse is BC(refer the attached figure )
therefore , Cosec ∠B = BC/AC
⇒Cosec ∠B = 8/6
Cosec ∠B = 4/3
Thus Cosec ∠B equals 4 over 3
And we are given the same Cosec ∠B equals 4 over 3.
Hence option 4 is correct.
