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Taya2010 [7]
3 years ago
6

Angles ∝ 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 < ∝.
sin(7x - 15) = cos(3x + 5)

A) 10°
B) 35°
C) 55°
D) 80°
Mathematics
2 answers:
Nadya [2.5K]3 years ago
7 0
We know that
in a right triangle
(∝ + β)=90°-------> by complementary angles
so
sin ∝ = cos β
sin(7x - 15) = cos(3x + 5)
Let 
∝=7x-15
β=3x+5

therefore

(7x-15)+(3x+5)=90 \\ 10x-10=90 \\ 10x=90+10 \\ x= \frac{100}{10}
x=10°

∝=7x-15-----------> ∝=7*10-15-------> ∝=55°
β=3x+5------------> β=3*10+5-------> β=35°

the answer is
 β=35°

arlik [135]3 years ago
5 0
Ok so cos(x) = sin(90-x) so using that you can get sin(7x-15) = sin(90-(3x+5)) so 7x-15 = -3x+85. 10x = 100 and x = 10. Use that to find the 2 angles are 55 and 35
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Please help me with this
Llana [10]
4 unknowns needs 4 equations. I'll call the unknown numbers a,b,c,d in that order left to right.

4 + a = b
a + b = c
b + c = d
c + d = 67

let's use substitution to get rid to combine equations and get rid of variables.
If a + b = c then a = c - b
4 + (c - b) = b
4 + c = 2b

If b + c = d then b = d - c
4 + c = 2(d - c)
4 + c = 2d - 2c
4 + 3c = 2d

then we have c + d = 67 so c = 67 - d

4 + 3(67 - d) = 2d
4 + 201 - 3d = 2d
205 = 5d
d = 41

Should be easy now, subtract backwards.

67 - 41 = 26
41 - 26 = 15
26 - 15 = 11
15 - 11 = 4

4, 11, 15, 26, 41, 67


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Answer:

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