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Snowcat [4.5K]
4 years ago
7

Two goals post are 8m apart. A footballer is 34m from one and 38m from the other. Within what angle must he kick the ball if he

is to score a goal?​
Mathematics
1 answer:
dmitriy555 [2]4 years ago
4 0

Answer:

  11.06°

Step-by-step explanation:

The law of cosines can be used to find the angle. The sides adjacent to that angle are a=34, b=38, and the side opposite is c=8. Then the angle is found from ...

  c² = a² +b² -2ab·cos(C)

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((34² +38² -8²)/(2·34·38)) = arccos(317/323)

  C ≈ 11.06°

From the footballer's viewpoint, the goal posts are 11.06° apart.

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Answer:

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<em>step by step...solving </em>

<em>10 + 4</em>\sqrt{6}<em />

<em>add/subtract </em>\sqrt{6}<em>² = 6</em>

<em>=10 + 4</em>\sqrt{6}<em> + </em>\sqrt{6}<em>² - 6</em>

<em>Refine</em>

<em>= </em>\sqrt{6}<em> ² + 4</em>\sqrt{6}<em> + 4</em>

<em>rewrite </em><em>↑</em><em> as </em>\sqrt{6}<em>² + 2</em>\sqrt{6}<em> * 2 + 2²</em>

<em>apply Perfect Square Formula (a + b)² = a² + 2ab +²</em>

<em>a = </em>\sqrt{6}<em>, b=2</em>

<em>= (</em>\sqrt{6}<em> + 2)²</em>

<em>= </em>\sqrt \sqrt({6}+ 2)<em>2square    </em>

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<em>apply radical rule </em>\sqrt[n]{a^{n} } = a<em>, assuming a ≥ 0</em>

<em>= </em>\sqrt{6} + 2<em />

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5 0
3 years ago
Oh freight elevator can hold a maximum weight of 3500 pounds and delivery man weighs 200 pounds is delivering curtains that each
mario62 [17]

Answer:

200+48n\leq 3500

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Step-by-step explanation:

  • The freight elevator can hold a maximum weight of 3500 pounds
  • The delivery man weighs 200 pounds
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Let the number of cartons he can safely put on the elevator at one time=n

Total weight of Carton=48n

Since the weight of the man and the cartons combined must not be more than 3500 pounds,

Therefore,an inequality that represents the situation is:

200+48n\leq 3500

We can solve for n if required

200-200+48n\leq 3500-200\\48n\leq 3200\\\text{Divide both sides by 48}\\n\leq66.7

The delivery man can safely carry 66 Cartons.

4 0
3 years ago
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AysviL [449]

Answer:

Step-by-step explanation:

From the given triangles in the picture attached,

∠A ≅ ∠X [Given]

∠B ≅ ∠Y [Given]

By AA property of similarity of the triangles, both the triangles will be similar.

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Similarity statement:

Corresponding sides of these similar triangles will be proportional.

\frac{XZ}{AB}= \frac{ZY}{BC}=\frac{XY}{AC}

Similarity ratio:

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3 years ago
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Answer:

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