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2 years ago

A map has a scale of 1:200000 How far is it from Belfast to Larne in Km if the distance on the map is 7.8cm

Mathematics

1 answer:

vivado [14]2 years ago

6 0

Answer:

15.6km

Step-by-step explanation:

Given the map scale 1:200000

1cm on the map represents 200000 cm on ground or in actual distance

Hence, if distance from Belfast to Larne is 7.8vm on map ;

Actual distance will be :

7.8 * 200000 = 1560000 cm

Converting to km :

Recall :

1000 m = 1km

100 cm = 1 m

Hence,

100000 cm = 1km

Therefore, (1560000 / 100000) km

= 15.6km

Hence, distance between Belfast and Larne is 15.6km

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2 years ago

A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of

Gwar [14]

$\bold{\huge{\underline{ Solution}}}$

<h3>Given :-</h3>

A marker in the center of the fairway is 150 yards away from the centre of the green
While standing on the marker and facing the green, the golfer turns 100° towards his ball
Then he peces off 30 yards to his ball

We have to find the distance between the golf ball and the center of the green .

<h3>Let's Begin :-</h3>

Let assume that the distance between the golf ball and central of green is x

Here, 

Distance between marker and centre of green is 150 yards
That is, Height = 150 yards
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That is, Base = 30 yards

According to the law of cosine :-

$\bold{\red{ a^{2} = b^{2} + c^{2} - 2ABcos}}{\bold{\red{\theta}}}$

Here, a = perpendicular height
b = base
c = hypotenuse
cos theta = Angle of cosine

So, For Hypotenuse law of cosine will be :-

$\sf{ c^{2} = a^{2} + b^{2} - 2ABcos}{\sf{\theta}}$

Subsitute the required values,

$\sf{ x^{2} = (150)^{2} + (30)^{2} - 2(150)(30)cos}{\sf{100°}}$

$\sf{ x^{2} = 22500 + 900 - 900cos}{\sf{\times{\dfrac{5π}{9}}}}$

$\sf{ x^{2} = 22500 + 900 - 900( - 0.174)}$

$\sf{ x^{2} = 22500 + 900 + 156.6}$

$\sf{ x^{2} = 23556.6}$

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PtichkaEL [24]

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