Question

Треугольник ABC AC=5см Угол A=38 градусов Угол B=87 градусов Найти S

Answer 1

S=1/2*a*b*sinC
a=4.1
b=5
По теореме синуса и косинуса я нашел а и б
После чего 
S=1/2*4.1*5*sin55
S=8.3968

Answer 2

Problem Analysis

We are given a triangle ABC with side AC measuring 5 cm, angle A measuring 38 degrees, and angle B measuring 87 degrees. We need to find the area of the triangle (S).

Solution

To find the area of the triangle, we can use the formula: S = 0.5 * AC * BC * sin(A), where BC is the unknown side of the triangle.

To find BC, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant. In this case, we can use the ratio: BC / sin(B) = AC / sin(A).

Let's calculate BC using the law of sines and then use it to find the area of the triangle.

Calculation

Using the law of sines, we have: BC / sin(B) = AC / sin(A)

Substituting the given values: BC / sin(87) = 5 / sin(38)

Now, we can solve for BC: BC = (5 * sin(87)) / sin(38)

Using a calculator, we find that BC ≈ 8.33 cm.

Now, we can calculate the area of the triangle using the formula: S = 0.5 * AC * BC * sin(A)

Substituting the given values: S = 0.5 * 5 * 8.33 * sin(38)

Using a calculator, we find that S ≈ 10.42 square cm.

Answer

The area of triangle ABC is approximately 10.42 square cm.