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Mrac [35]
3 years ago
13

Sam used his calculator to find the answer and wrote down cos 1.75 = 0.999. Does this seem like a reasonable answer to you? What

might he have done wrong on his calculator?
Mathematics
1 answer:
Elan Coil [88]3 years ago
7 0

 

Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.

What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:

θ = 1.75 rad (180° / π rad)

θ = 100.2676

<span>cos 100.2676 = -0.1782   which is now correct since it is nearer to zero</span>

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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T
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Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180                      ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}

105^{\circ}+ m\angle B=180^{\circ}

Simplify:

m\angle B=75^{\circ}

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle  to the sines of its angles.

\frac{\sin A}{BC} = \frac{\sin C}{AB}

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}

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BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}

BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798 unit

Similarly for  AC:

\frac{\sin B}{AC} = \frac{\sin C}{AB}

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}

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AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}

AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283 unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

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Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

A = \frac{1}{2} \times AB \times AC \times \sin A

Substitute the values in above formula to get area;

A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}

A = 4 \times 10.9283 \times 0.86602540378

Simplify:

Area of triangle ABC = 37.856 (approx) square unit





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