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zimovet [89]
3 years ago
13

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β

if β < α. sin(3x − 27) = cos(5x + 5)
A) 14°
B) 15°
C) 75°
D) 76°
Mathematics
1 answer:
ElenaW [278]3 years ago
5 0

Answer:

A) 14°

Step-by-step explanation:

If α and β are the two angles other than 90° in a right triangle, then we have the relation between α and β as, α+β=90°.

Therefore, Sin α = Sin (90° -β) =Cos β.

So, we can write the reverse as if Sin α = Cosβ, then we have α + β =90°.

It is given that, Sin (3x-27) = Cos (5x+5).

Hence, we can write (3x-27) + (5x + 5) = 90

⇒ 8x = 90+27-5 =112

⇒ x = 14°

Therefore, option A. is correct. (Answer)

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Answer:

x= 81°, z= 99°, y°=68°

Step-by-step explanation:

considering the part of the triangle where 36° , 63° and x° is located as ΔABC.

to find the measure of x we use angle sum property.

We know that the sum of the angles of a triangle is always 180°. Therefore, if we know the two angles of a triangle, and we need to find its third angle, we use the angle sum property. We add the two known angles and subtract their sum from 180° to get the measure of the third angle.

so,

∠A + ∠B +∠C = 180°

36° + 63° + x° = 180°

99° + x° = 180°

x° = 180 - 99

x° = 81°

When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.

x° + z° = 180°

81° + z = 180°

z= 180 - 81

z= 99°

considering the next part of the triangle where 13° , z° and y° is located as ΔACD

to find the measure of y we use angle sum property.

∠A + ∠C + ∠D = 180°

13° + z° + y° = 180°

13°+99°+y°= 180°

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y°= 180- 112

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Answer:

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Step-by-step explanation:

You are given 3x-4y<16 and we want to see which of the ordered pairs is a solution.

These ordered pairs are assumed to be in the form (x,y).

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16<16 is not true so (0,-4) is not a solution of the given inequality.

B. (4,-1)?

3x-4y<16 with (x=4,y=-1)

3(4)-4(-1)<16

12+4<16

16<16 is not true so (4,-1) is not a solution of the given inequality.

C. (-3,-3)?

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D. (2,-3)?

3x-4y<16 with (x=2,y=-3)

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