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aliina [53]
3 years ago
6

1) Solve for Side A 2) Solve for Angle B

Mathematics
2 answers:
motikmotik3 years ago
8 0

Answer:

1) 42.51

2) 39.76

algol [13]3 years ago
5 0

Answer:

solution given;

let

AB=a

AC=b=30ft

AB=c=20ft

<A=115°

By using Cosine rule.

a²=b²+c²-2bc cos angle

a²=30²+20²-2*30*20 Cos 115°

a²=1807.1419

a=√[1807.1419]

a=42.51

Side A is 42.51ft.

Again

Cos B=\frac{a²+c²-b²}{2ac}

Cos B=\frac{42.51²+20²-30²}{2*42.51*20}

Cos B=0.7687

<B=Cos -¹(0.7687)

<B=39.46°

Angle B is 39.46

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In parallelogram ABCD, AD = 12 in, m∠C = 46º, m∠DBA = 72º. Find the area of ABCD
dmitriy555 [2]

Answer:

The area of   parallelogram ABCD  is78.42 \mathrm{in}^{2}

Explanation:

Given:

AD = 12 in

m \angle C=46^{\circ}

m \angle D B A=72^{\circ}

To Find:

The area of   parallelogram ABCD=?  

Solution:

When we construct the parallelogram with the given data, we get a parallelogram formed by 12 cm as one side and an angle with 46 degrees.  

The area of the parallelogram can be calculated by a b * \sin (a n g l e)

Substituting the value of a=12  we have

\text { Area of parallelogram }=12 * \text { bsin } 46

<u>To find  the value of b, </u>

We know that area of a triangle can be expressed as,

\text { Area of triangle }=(A b / 2) \sin (\text {angle})

So,

(12 * B D / 2) * \sin 46=(A B * B D / 2) * \sin 72

Cancelling BD and 2 on both sides we get,  

12 * \sin 46=A B * \sin 72

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b=\frac{12 \sin 46}{\sin 72}

Substituting the value of b,

=12 *\left(\frac{12 \sin 46}{\sin 72}\right) * \sin 46

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