# what is is the measure of the larger acute angle and other stuff ?

1) in a right triangle the measures of the acute angles are in the ratio 3:7 find the measure of the larger acute angle

2)in a right triangle the measure of one acute angle is 30 less than twice the measure of the other acute angle find the measure of each angle

3)the lengths of two side of a triangle are 15 and 8 use an inequality to express the range of the length of the third side

4)the length of the base of an isosceles triangle is 12 what can be said about the length of the legs of the triangle ?

Relevance

Problem One

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Let the smallest angle = x

3/7 = x / (90 - x) [ x is opposite the 3]

cross multiply

3*(90 - x) = 7x Remove the brackets

270 - 3x = 7x add 3x

270 = 10x

x = 27 degrees.

The other angle = 90 - 27 = 63

Check

27 / 63 divide by 9

3 / 7

Problem Two

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Let the first angle = x

Let the other angle = 2x - 30

x + 2x - 30 = 90

3x - 30 = 90 Add 30

3x = 90 + 30

3x = 120 divide by3

x = 40

Check

40 + 2*40 - 30

40 + 80 - 30

40 + 50

90

Problem Three

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The smallest that the third side can be is 7 because because 8 + 7 would make 15. So you have to be just a fraction over 7.

The largest value that the third side can be 8+ 15 = 23. The inequality is

7 < x < 23

Problem Four

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Both equal sides have to be greater than x. otherwise there is no restriction.

x>6

• (1) let the acute angles are 3x & 7x

so 3x + 7x = 90

or x= 9

so larger acute angle = 7* 9 = 63deg. answer

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(2) let acute angles are x & (2x- 30)

so x + 2x - 30 = 90

3x = 120

x= 40

so angles are 40 & (80-30) i.e 50 answer

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