John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground opposite
a big tree. The steps John would use to find the measure he wants are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.
The steps John would use to measure the width of the stream are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.
1. Step 1
5
John measures the distance between the two stakes.
2. Step 2
2
John uses a compass to walk away from the stake at a right angle.
3. Step 3
4
John multiplies the distance between the two stakes by 1.7 to find the distance.
4. Step 4
3
John drives a second stake in the ground.
5. Step 5
1
On the path John walks until he finds a line of sight to the tree that equals 60 degrees.
6. Step 6
6
John drives a stake opposite the tree to establish a line between two points.
The steps John would use to measure the width of the stream are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.
1. Step 1
5
John measures the distance between the two stakes.
2. Step 2
2
John uses a compass to walk away from the stake at a right angle.
3. Step 3
4
John multiplies the distance between the two stakes by 1.7 to find the distance.
4. Step 4
3
John drives a second stake in the ground.
5. Step 5
1
On the path John walks until he finds a line of sight to the tree that equals 60 degrees.
6. Step 6
6
John drives a stake opposite the tree to establish a line between two points.
2 answers:
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Answer:
Option (C)
Step-by-step explanation:
Given sides of a triangle are 2, and
.
Option (A).
If the triangle is a right triangle.
By Pythagoras theorem,
(Longest side)² = (Leg 1)² + (Leg 2)²
19 = 4 + 12
19 = 16
Not true.
Therefore, its not a right triangle.
Option (B).
If it is a triangle following conditions will be followed.
1). a + b > c
2). b + c > a
3). a + c > b
For the given sides of the triangle,
1). 2 + √12 > √19 [True]
2). 2 + √19 > √12 [True]
3). √12 + √19 > 2 [True]
Therefore, the given measures of the sides will form a triangle.
Option (C)
By Pythagorean inequality theorem,
If c² = a² + b² → Right triangle
If c² > a² + b² → Obtuse triangle
If c² < a² + b² → Acute triangle
Since, (√19)² > 2² + (√12)² → 19 > 4 + 12
Therefore, the given triangle is an Obtuse triangle.
Option (D).
Not true. It's an obtuse triangle.