Given the triangle below, which of the following is a correct statement?

right triangle abc with ab measuring 5, ac measuring 6, and bc measuring 8.

cot angle b equals 6 over 5
csc angle c equals 3 over 4
cot angle c equals 8 over 5
csc angle b equals 4 over 3

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.

true

explanation:

is there a picture

step-by-step explanation: