Answer:
x° = 37°
Step-by-step explanation:
* Lets revise some facts of a circle
- The secant is a line intersect the circle in two points
- If two secants intersect each other in a point outside the circle,
then the measure of the angle between them is half the difference
of the measures of their intercepted arcs
* Now lets solve the problem
- There is a circle
- Two secants of this circle intersect each other in a point outside
the circle
∴ The measure of the angle between them = 1/2 the difference of the
measures of their intercepted arcs
∵ The measure of the angle between them is x°
∵ The measures of their intercepted arcs are 26° and 100°
- Use the rule above to find x
∴ x° = 1/2 [ measure of the large arc - measure of small arc]
∵ The measure of the large arc is 100°
∵ The measure of the small arc is 26°
∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°
∴ x° = 37°
Vic and Dan are 2, 897m apart.
<h3>How to determine the distance</h3>
It is important to note that the distance between Vic and Dan is the base of CN
Let's say the distance to Dan is x
The distance to Vic is y
Using cosine ratio, we have
cos α = opposite / adjacent
α = 72°
opposite = 553. 3cm
Adjacent = x
cos 72° = 
Cross multiply
× 
= 
m
The distance to Vic is y
Using the cosine ratio, we have
Cross multiply
m
To determine how far apart Vic and Dan, we use = x + y
= 1790. 61 + 1106. 6
= 2, 897. 21m
= 2, 897m
Thus, Vic and Dan are 2, 897m apart.
Learn more about bearing and distance here:
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