Helpful for grade 9 teachers

1. REAL-LIFE PROBLEMS
INVOLVING RIGHT
TRIANGLES
9th Grade
BY:
QUARTER 4
Math Teacher

2. OPENING PRAYER!

3. FACT
OR
BLUFF?

4. FACT OR BLUFF?

5. FACT OR BLUFF?

6. FACT OR BLUFF?

7. Trigonometric
ratios
Lesson Recap


8. Trigonometric ratios
Sin θ Opposite side of θ/Hypotenuse
Cos θ Adjacent side of θ/Hypotenuse
Tan θ Opposite side of θ/Adjacent side of θ
Cot θ Adjacent side of θ/Opposite Side of θ
Sec θ Hypotenuse/Adjacent side of θ
Cosec θ Hypotenuse/Opposite side of θ
The six ratios are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec)
and secant (sec)≈

9. Lesson Proper


10. OBJECTIVES:
At the end of the lesson, you are able to:
A. Recall the concept of trigonometric ratio, angle of
elevation and angle of depression;
B. Uses trigonometric ratios to solve real-life problems
involving right triangles (M9GE-IVe-1); and
C. Solve real – life problems involving angle of
elevation and angle of depression.

11. Introduction
The concepts on trigonometric
ratios and angles of elevation and
depression are necessary in
solving word problems involving
right triangles. Many real-life
problems involving right triangles
are based on these concepts.

12. VIDEO DISCUSSION

13. Activity 1: Accessibility
The Philippines’ Accessibility Law or Batas Pambansa 344 (BP
344) provides regulations designed to make public buildings
accessible to all. Under this act, the slope of a ramp designed for
those with mobility disabilities must not exceed a 1:12 ratio. This
means that for every 12 units of horizontal run, the ramp can rise
or fall not more than 1 unit. A ramp forms a right triangle when
viewed from the side.
WHAT’S NEW?

14. A person on a lake sees a plane flying
overhead. The angle formed by his line
of sight to the plane is 390. if the plane
is flying about 5000 ft., find the
horizontal ground distance between the
person and the plane.
ILLUSTRATIVE EXAMPLE #1

16. ILLUSTRATIVE EXAMPLE #2
A seesaw has a plank of 4.5 𝑚 long
which is supported by a pivot at its
center and moves in a vertical plane
above the pivot. If the height of the pivot
pillar above the ground is 1 𝑚, through
what maximum angle can the seesaw
beam move?

17. ILLUSTRATIVE EXAMPLE #2

18. ACTIVITY TIME!
Group Activity
Hola

20. RUBRICS

21. Finding practical
applications of concepts
and skills in daily living!
Question:
1. Is it important to adopt a procedure in
solving problems involving right
triangles using trigonometric ratios?
Why?
2. How can this concept on trigonometric
ratios and solving right triangles be
used to solve real-life problems?

22. GENERALIZATION
How to solve problems
involving right triangles?

23. Answer to generalization

24. Assessment
Directions:
Read and analyze the problems carefully
and choose the letter that corresponds to
your answer. Write your answer on a
separate sheet.

25. Assessment
1. A kite in the air has its 60 m string to the
ground and makes an angle of elevation of 45o.
About how high is the kite with the ground?
a.28.1 m
b.31.4 m
c.39.7 m
d.42.4 m

26. Assessment
For items 2 to 3, refer to the problem below.
A tree that was broken by a string wind brought
by the typhoon has its top touch the ground 13 m
from the base. It makes an angle with the ground
measuring 29o.

27. Assessment
2. If y is the height of the broken tree left
standing vertically on the ground, which equation
will help you find its height?
a.Sin 290 = y/13
b.Cos 290 = 13/y
c.Tan 290 = y/13
d.Sec 290 = 13/y

28. Assessment
3. How tall was the tree before it was
broken?
a.19.8 m
b.22.1 m
c.33.7 m
d.41.2 m

29. Assessment
For items 4 to 5, refer to the problem below.
To measure the width of the river, a surveying technique
is used. Suppose a stake is planted across opposite
sides of the river and an angle of 82° at a distance 50 𝑚
to the left of the stake is measured between two stakes.

30. Assessment
4. If w represents the width of the river, which
equation will help you solve the given problem?
a.Sin 82o = w/50
b.Cos 82o = 50/w
c.Tan 82o = w/50
d.Sec 82o = 50/w

31. Assessment
5. Find the width of the river
a.252 m
b.355.8 m
c.430.2 m
d.451.7 m

32. Hi, kids!
CONGRATULATIONS!

33. ASSIGNMENT
The basketball ring is 10 ft. above the ground. The free
throw is 15 ft. from the basketball ring. The eyes of the
basketball player are 6 ft. above the ground.
1. What is the vertical distance between the player’s
line of sight and basketball ring?
2. What is the angle of elevation of the player’s line of
sight when shooting a free throw to the basketball
ring?

34. CREDITS: This presentation template was
created by Slidesgo, and includes icons by
Flaticon and infographics & images by Freepik
Thanks
GODBLESS!