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seaotter7140
18.03.2021 •
Mathematics
A guide into how to use law of sines or cosines would be greatly appreciated.
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Ответ:
RS = 22.5 feet, RT = 12.5 feet, and <R =![34^{o}](/tpl/images/1195/4379/94674.png)
Step-by-step explanation:
Cosine rule can be applied only when given the three sides of a triangle, or two sides and an included angle. Otherwise, sine rule is applied.
i. <R + <T + <S = 180 (sum of angles in a triangle)
<R + 116 + 30 = 180
<R = 180 - 146
= 34
<R =![34^{o}](/tpl/images/1195/4379/94674.png)
In the given question, since we have two angles and one side we apply the sine rule.
ii.
= ![\frac{RS}{Sin T}](/tpl/images/1195/4379/8cc34.png)
RS =![\frac{14*0.8988}{0.5592}](/tpl/images/1195/4379/5424d.png)
= 22.5021
RS = 22.5 feet
iii. Also,
RT =![\frac{14*Sin 30}{Sin 34}](/tpl/images/1195/4379/5a21b.png)
=![\frac{14*0.5}{0.5592}](/tpl/images/1195/4379/70932.png)
= 12.5179
RT = 12.5 feet
Thus,
RS = 22.5 feet, RT = 12.5 feet, and <R =
.
Ответ:
The formula used will be:
tan 42° = y/115
Step-by-step explanation:
Lets simplify the the question.
We have a boat which is situated at 115 meters away from a light house. It forms the base of the right angled triangle.
We need to find the distance from the bottom of the light house to the top of the light house. This distance is the height of the lighthouse, which forms the perpendicular side of the right angled triangle.
The distance between boat and top of the lighthouse is unknown, it forms the hypotenuse.
The angle of elevation, which is the angle between base and hypotenuse, is given as 42°.
The right angled formed is shown below.
We know that
tanθ = Perpendicular / Base
tan42 = height / 115
If height= y
tan 42° = y/115
Solve for y.
y = 103.55 meters