Question

В abc b=90 sina=4/7 ac =28 найдите ab

Answer 1

Т.к. угол А острый, то косинус его тоже число положительное, равное √(1-16/49)=√33/7

тогда АВ равно произведению АС на косинус угла А

АВ=28*√33/7=4√33

Answer 2

To find the length of side AB in the triangle ABC, we can use the Pythagorean theorem and trigonometric ratios. Since we are given the length of side AC and angle B, we can use the sine function to find the length of side BC, and then use the Pythagorean theorem to find the length of side AB.

1. Find the length of side BC: We are given that b = 90 degrees and sin(a) = 4/7. Using the sine function, we have: sin(a) = BC / b 4/7 = BC / 90

Now, solve for BC: BC = (4/7) * 90 BC = 360/7

2. Use the Pythagorean theorem to find the length of side AB: In a right-angled triangle, the Pythagorean theorem states: c^2 = a^2 + b^2

where c is the hypotenuse (AC in this case), and a and b are the other two sides (AB and BC).

a^2 = c^2 - b^2 a^2 = 28^2 - (360/7)^2

Now, calculate a: a = √(28^2 - (360/7)^2) a ≈ 23.90 (rounded to two decimal places)

So, the length of side AB is approximately 23.90 units.