Question

a=13 c=15 A=53 Two sides and an angle​ (SSA) of a triangle are given. Determine whether the given measurements produce one​ triangle, two​ triangles, or no triangle at all. Solve each triangle that results.

Answer 1

The given measurement will produce only 1 triangle

Explanation:

Given:

a = 13

c = 15

∠A = 53°

now, applying the law of sine, we have

(a/sinA) = (c/sinC)

on substituting the values, we get

(13/sin53°) = (15/sinC)

or

sinC = 0.921

or

C = 67.14°

also, sum of all the angles of a triangle = 180°

thus,

∠A + ∠B + ∠C = 180°

53° + 67.14° + ∠B = 180°

or

∠B = 59.85°

now,

again applying the law of sine, we have

(a/sinA) = (b/sinB)

on substituting the values, we have

(13/sin53) = (b/sin59.85°)

or

b = 14.07

now, we have all the dimension of the triangle and have obtained the unique values,

Therefore, the given measurement will produce only 1 triangle