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e-lub [12.9K]
3 years ago
9

Use the diagram to complete the statement. Triangle J K L is shown. Angle K J L is a right angle. Angle J K L is 52 degrees and

angle K L J is 38 degrees. Given △JKL, sin(38°) equals cos(38°). cos(52°). tan(38°). tan(52°).

Mathematics
1 answer:
zzz [600]3 years ago
6 0

Answer:

\bold{sin(38^\circ)=cos(52^\circ)}

Step-by-step explanation:

Given that \triangle KJL is a right angled triangle.

\angle JKL = 52^\circ\\\angle KLJ = 38^\circ

and

\angle KJL = 90^\circ

Kindly refer to the attached image of \triangle KJL in which all the given angles are shown.

To find:

sin(38°) = ?

a) cos(38°)

b) cos(52°)

c) tan(38°)

d) tan(52°)

Solution:

Let us use the trigonometric identities in the given \triangle KJL.

We have to find the value of sin(38°).

We know that sine trigonometric identity is given as:

sin\theta =\dfrac{Perpendicular}{Hypotenuse}

sin(\angle JLK) = \dfrac{JK}{KL}\\OR\\sin(38^\circ) = \dfrac{JK}{KL}....... (1)

Now, let us find out the values of trigonometric functions given in options one by one:

cos\theta =\dfrac{Base}{Hypotenuse}

cos(\angle JLK) = \dfrac{JL}{KL}\\OR\\cos(38^\circ) = \dfrac{JL}{KL}....... (2)

By (1) and (2):

sin(38°) \neq cos(38°).

cos(\angle JKL) = \dfrac{JK}{KL}\\OR\\cos(52^\circ) = \dfrac{JK}{KL} ...... (3)

Comparing equations (1) and (3):

we get the both are same.

\therefore \bold{sin(38^\circ)=cos(52^\circ)}

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