A wire is attached to the top of a flag pole. The wire meets the ground 4 meters from the flag pole. The wire makes a 45° angle with the flag pole. How tall is the flag pole?
3 Answers
The high of flag pole is
Explanation:
We know that
In the right triangle We need to find h and b is 4 m.
The oposite angle to h is 45º. Thus
Trasposing we find
The flagpole is
Explanation:
The wire, the flagpole, and the ground make up the three sides of a triangle.
- One angle of this triangle is given as
#45^o# . - The angle of the flagpole with the ground must be
#90^o# . - So the last angle must be
#45^o# .
Because of the right angle
Because both of the other angles are the same (both are
This particular kind of right triangle is called a
The measurements of these triangles are known by memorization:
The
- It forms half a square, cut in half along the diagonal, so it is a
#"right triangle"# . - This diagonal line forms the
#"hypotenuse"# of the triangle. - The sides
#s# (the legs) are the same as each other, so
it is an#"isosceles right triangle."# - The length of the hypotenuse is always
#ssqrt(2)#
Here is a diagram of the
http://www.dummies.com/education/math/geometry/identifying-the-45-45-90-degree-triangle/
Note:
Taking five minutes now to memorize this information will save you hours.
On timed standardized tests such as the SAT, ACT, or GRE, you can complete many problems in seconds while other students are still burning up their minutes solving the Pythagorean Theorem.
In this problem, one of the sides (the side along the ground) is Given as
Because both of the sides are the same, then the other side (the flagpole) must also be
Answer:
The flagpole is
Extra credit:
The wire is the hypotenuse, whose length is
So the hypotenuse is
The flag pole is
Explanation:
We need to make an assumption here - that the flagpole is perpendicular to the horizontal ground.
If one angle is
Two of the angles are equal so this is an Isosceles triangle, in fact, a right-angled isosceles triangle.
In an isosceles triangle, there are two equal sides and two equal angles opposite the equal sides.
There are no calculations necessary at all - you just need to recognise what type of triangle it is.
The equal sides are the arms of the
They are both
The wire from the top of the pole to the ground represents the hypotenuse. It will be longer than the other sides.