2 Two of the angles of this polygon are 100°. All the other angles are equal. (100° 1000 Calculate the size of the unmarked angl
1 answer:
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Answer:
θ ≈ 17.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan θ = =
=
, then
θ = (
) ≈ 17.1° ( to the nearest tenth )
The answer is 6.7 mi.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²)<span>:
c</span>² = a² + b²<span>
First, we need to express symbols:
b - side of the right triangle (distance </span><span>between police department and Freeport High School).
a1 - </span>side of the first right triangle (distance between library and Freeport High School).<span>
a2 - </span><span>side of the second right triangle (distance between park and Freeport High School).
c1 - hypotenuse of the first triangle (distance between </span>police<span> department and library).
c2 - </span>hypotenuse of the second triangle (distance between police<span> department and park).
Therefore, we need to calculate c2.
It is given:
a2 = 6 mi
a1 = 4 mi
c1 = 5 mi
First, let's calculate b, which is a common side for two triangles:
</span>c1<span>² = a1² + b²
</span>b² = c1<span>² - a1²
</span>b² = 5<span>² - 4²
</span>b² = 25<span> - 16
</span>b² = 9
√b² = √9
b = 3.
We know b, now we can calculate c2:
c2<span>² = a2² + b²
</span>c2<span>² = 6² + 3²
</span>c2<span>² = 36 + 9
</span>c2<span>² = 45
</span>√c2<span>² = </span>√45
c2 = 6.7
The distance between police department and park is 6.7 miles.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²)<span>:
c</span>² = a² + b²<span>
First, we need to express symbols:
b - side of the right triangle (distance </span><span>between police department and Freeport High School).
a1 - </span>side of the first right triangle (distance between library and Freeport High School).<span>
a2 - </span><span>side of the second right triangle (distance between park and Freeport High School).
c1 - hypotenuse of the first triangle (distance between </span>police<span> department and library).
c2 - </span>hypotenuse of the second triangle (distance between police<span> department and park).
Therefore, we need to calculate c2.
It is given:
a2 = 6 mi
a1 = 4 mi
c1 = 5 mi
First, let's calculate b, which is a common side for two triangles:
</span>c1<span>² = a1² + b²
</span>b² = c1<span>² - a1²
</span>b² = 5<span>² - 4²
</span>b² = 25<span> - 16
</span>b² = 9
√b² = √9
b = 3.
We know b, now we can calculate c2:
c2<span>² = a2² + b²
</span>c2<span>² = 6² + 3²
</span>c2<span>² = 36 + 9
</span>c2<span>² = 45
</span>√c2<span>² = </span>√45
c2 = 6.7
The distance between police department and park is 6.7 miles.