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3 years ago

NEED GEO HELP URGENT?

Mathematics

1 answer:

m_a_m_a [10]3 years ago

4 0

Secant and tangent theorem: Square of measure of tangent is equal to the product of length of whole secant and length of exterior secant segment, i.e.

$\text{ tangent }^2=\text{whole secant}\cdot \text{exterior secant}$ .

The whole secant wuth exterior secant 4 cm is 4+x cm. Tangent is 7 cm. Using previous theorem, you can get that

$7^2=(4+x)\cdot 4$ .

Solve this equation:

$49=16+4x,\\ 4x=49-16,\\ 4x=33,\\ x=8.25\approx 8.3$ cm.

Answer: x=8.3 cm.

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Find the measure of DAE

kupik [55]

In the given diagram, the measure of angle DAE is 48°

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From the question, we are to determine the measure of angle DAE

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3 years ago

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A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns

uysha [10]

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

$\angle A+40+100=180$

$\angle A+140=180$

$\angle A=180-140$

$\angle A=40$ degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

$\implies BC=AC$

Now, Sine law

$\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}$

Using the sine law

$\frac{BC}{sin 40}=\frac{AB}{sin 100}$

$\frac{BC}{sin 40}=\frac{8}{sin 100}$

$BC=\frac{8\times sin40}{sin 100}$

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

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3 years ago