Refer to right triangle ABC with C = 90^{circ}. Begin each problem by drawing a picture of the triangle with both the given and askedfor information labeled appropriately. Also, write your answers for angles in decimal degrees. If a = 42.3 inches and b = 32.4 inches, find B

Question

Refer to right triangle ABC with

C = 90^{\circ} .

Begin each problem by drawing a picture of the triangle with both the given and askedfor information labeled appropriately.
Also, write your answers for angles in decimal degrees.
If

a = 42.3 i n c h e s a n d b = 32.4

inches, find B

Answer 1

Data analysis
Given right angled triangle at C for a triangle $△ A B C .$
And $a = 42.3$ inches
$b = 32.4$ inches
To find angle at B.
The triangle with above data is as follows

Solution
Since the give triangle is right angled,
Applying Pythagoras theorem,
$c^{2} = a^{2} + b^{2}$
$= {42.3}^{2} + {32.4}^{2}$
$= 1789.29 + 1049.76$
$\Rightarrow c = \sqrt{2839.05} = 53.2827364$
Hence the length of $A B = c = 53.28$ inches
(Rounding to two decimals)
By sine law,
$\sin B = \frac{o p p o s i t e s i d e}{h y p o t e n u s e}$
$= A C / A B$
$= b / c$
$= 32.4 / 53.28$
$\Rightarrow ∠ B = \arcsin (0.608108) = {37.4528244}^{\circ}$
Hence the angle at B is ${37.24}^{\circ}$
(Rounding to two decimals)

Refer to right triangle ABC with C = 90^{circ}. Begin each problem by drawing a picture of the triangle with both the given and askedfor information labeled appropriately. Also, write your answers for angles in decimal degrees. If a = 42.3 inches and b = 32.4 inches, find B

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Refer to right triangle ABC with C = 90^{circ}. Begin each problem by drawing a picture of the triangle with both the given and asked­for information labeled appropriately. Also, write your answers for angles in decimal degrees. If a = 42.3 inches and b = 32.4 inches, find B

Expert Answer

Not exactly what you’re looking for?

Relevant Questions

Refer to right triangle ABC with C = 90^{circ}. Begin each problem by drawing a picture of the triangle with both the given and askedfor information labeled appropriately. Also, write your answers for angles in decimal degrees. If a = 42.3 inches and b = 32.4 inches, find B