The angles shown above are acute and sin(a^∘)=cos(b^∘) . If a=4 k-22 and b=6 k-13 what is the va

Name: Problem 23, Chapter :
Uploaded: 2019-05-13T21:56:10-08:00
Duration: 1 min 49 s
Channel: Lily An
Description: The angles shown above are acute and sin(a^∘)=cos(b^∘) . If a=4 k-22 and b=6 k-13 what is the value of k ? A) 4.5 B) 5.5 C) 12.5 D) 21.5

step 1 Okay, so for this, it says that the sign of A plus the cosine of B are equal. So sign of A is eq

Question

The angles shown above are acute and $\sin \left(a^{\circ}\right)=\cos \left(b^{\circ}\right) .$ If $a=4 k-22$ and $b=6 k-13$ what is the value of $k ?$ A) 4.5 B) 5.5 C) 12.5 D) 21.5

   The angles shown above are acute and
$\sin \left(a^{\circ}\right)=\cos \left(b^{\circ}\right) .$ If $a=4 k-22$ and $b=6 k-13$
what is the value of $k ?$
A) 4.5
B) 5.5
C) 12.5
D) 21.5

Instant Answer

Solved by Expert Lily An

05/13/2019

Step 1

We know that if $\sin \left(a^{\circ}\right)=\cos \left(b^{\circ}\right)$, then $a + b = 90^{\circ}$. Show more…

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The angles shown above are acute and $\sin \left(a^{\circ}\right)=\cos \left(b^{\circ}\right) .$ If $a=4 k-22$ and $b=6 k-13$ what is the value of $k ?$ A) 4.5 B) 5.5 C) 12.5 D) 21.5

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Key Concepts

Complementary Trigonometric Identity

This concept involves the relationship between the sine and cosine functions that states sin(?) is equal to cos(90° - ?) when the angle is measured in degrees. This identity is particularly useful when dealing with problems involving acute angles, as it allows for the conversion between sine and cosine functions by relating the angles as complementary to each other.

Solving Linear Equations

This concept refers to the process of finding the value of unknown variables in equations that are linear in nature, meaning the variable is not raised to any power greater than one. In the context of the given problem, forming one or more equations from the trigonometric identity and the provided expressions for the angles leads to an equation in k, which can then be solved through algebraic manipulation.

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