Ladder Heights, Trigonometric Graphs, Resultant Forces, and Volume Calculations: Summary of Given Data

Trigonometry Assignment
Student’s Name
Institution Affiliation

Task 1
Part a
I. How far up does the ladder reach
Using the sine rule , 1.4
Sinθ = 5
sin 90
Sinθ=1.4 sin 90
5 =0.28
θ=sin−1 0.28=16.26 °
Wall length=5 cos 16.26 ° =4.80 m
We obtain the same answer using Pythagoras theorem as follows.
x= √ 52−1.42=4.8 m
II. Minimum length of the ladder. Given that the value of height =4.5 and the
θ=90 °−74 °=16 °
cos ( 16 ° ) = 4.5
Ladder Length

Ladder Length= 4.5
cos ( 16° ) =4.68 m
III. The angle at which the ladder meets the horizontal ground, given that the ration for
ladder horizontal to vertical is 1:4
Tanθ= Opposite
Adjacent = 4
1 =4
θ=tan−1 (4)=75.96 °≅ 76.0°
Part b
I. 150 ° to radian
180 °=π radian,
Therefore, 150 °will be given by
150°
180° π = 5
6 π radian
II. Area of the region covered
Area=rad
2 π ∗π r2
¿ 5 π
6∗2 π ∗π∗122