Step 1:
Calculate the measure of angle ∠ABC
From the triangle in the question,
Step 2:
Calculate the value of AB using the cosine rule below
By substituting the values, we will have
![\begin{gathered} b^2=a^2+c^2-2\times a\times c\times\cos B \\ b^2=10^2+15^2-2\times10\times15\times\cos 115^0 \\ b^2=100+225-300\times(-0.4226) \\ b^2=325+126.78 \\ b^2=451.78 \\ \text{Square root both sides} \\ \sqrt[]{b^2}=\sqrt[]{451.78} \\ b=21.26\operatorname{km} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20b%5E2%3Da%5E2%2Bc%5E2-2%5Ctimes%20a%5Ctimes%20c%5Ctimes%5Ccos%20B%20%5C%5C%20b%5E2%3D10%5E2%2B15%5E2-2%5Ctimes10%5Ctimes15%5Ctimes%5Ccos%20115%5E0%20%5C%5C%20b%5E2%3D100%2B225-300%5Ctimes%28-0.4226%29%20%5C%5C%20b%5E2%3D325%2B126.78%20%5C%5C%20b%5E2%3D451.78%20%5C%5C%20%5Ctext%7BSquare%20root%20both%20sides%7D%20%5C%5C%20%5Csqrt%5B%5D%7Bb%5E2%7D%3D%5Csqrt%5B%5D%7B451.78%7D%20%5C%5C%20b%3D21.26%5Coperatorname%7Bkm%7D%20%5Cend%7Bgathered%7D)
Hence,
The distance of point A to point C is = 21.26km
Answer:
48559 if to the nearest whole number
48558.7 if to the nearest tenth
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Answer:
Step-by-step explanation:
Triangle ABC is an equilateral triangle, then:
=> angle ABC = angle BAC = angle ACB = 60 deg
AB // CE, according to alternative interior pair of angles theorem:
=> angle ACE = angle BAC = angle ABC = 60 deg (1)
B, C, and D are colinear, then:
angle ECD + angle ACE + angle ACB = 180 deg
=> angle ECD = 180 - angle ACE - angle ACB = 180 - 60 - 60 = 60 deg (2)
From (1) and (2):
=>angle ACE = angle ECD = 60 deg
