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

2 answers

Question:

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

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

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