Question

Step-by-Step explanation would be great!

If AB= 19 and BC = 8, find the measure of Angle A. Round to the
nearest tenth.
A
B

Answer 1

• A = 24.9°

Explanation:

To find:-

• The value of angle A .

Answer:-

We are given a right angled triangle, with AB = 19 and BC = 8 . We are interested in finding out the value of angle A .

• With respect to angle A , the sides BC is perpendicular , AC is base and AB is hypotenuse .
• Hypotenuse is the longest side in a right angled triangle opposite to 90° as side opposite to largest angle is largest.
• Here we are given the values of AB which is hypotenuse and BC which is perpendicular.
• So we would have to use a ratio in terms of hypotenuse and perpendicular.
• Hence here we should use the ratio of sine .In a right angled triangle sine is defined as the ratio of perpendicular and hypotenuse .

Mathematically,

`\longrightarrow\large\pmb{ \sin\theta =(perpendicular)/(hypotenuse)} \\`

On substituting the respective values, we have;

`\longrightarrow \sin A =(8)/(19) \\`

Take sin inverse on both the sides,

`\longrightarrow \sin^(-1)(\sin A ) = \sin^(-1)\bigg((8)/(19)\bigg) \\`

Simplify,

`\longrightarrow A =\sin^(-1)\bigg((8)/(19)\bigg) \\`

To find the value , we would have to use a calculator,

`\longrightarrow\large\pmb{\underline{\boxed{ A = 24.9^o}}} \\`

Therefore the approximate value of angle A is 24.9° to the nearest tenth .

Answer 2

• Angle A is approximately 24.9 degrees

========================

To find the measure of Angle A, we'll use the sine function from trigonometry. First, let's identify the sides of the triangle:

• Hypotenuse, AB = 19;
• Opposite side to Angle A, BC = 8.

Now we can use the sine function to find the measure of Angle A:

• sin(A) = opposite side / hypotenuse
• sin(A) = BC / AB
• sin(A) = 8 / 19
  

Now, to find the angle A, we need to take the inverse sine (arcsin) of the ratio:

• A = arcsin(sin(A))
• A = arcsin(8/19)

Using a calculator, we find:

• A ≈ 24.9 degrees

So, the measure of Angle A is approximately 24.9 degrees, rounded to the nearest tenth.