1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ICE Princess25 [194]
2 years ago
7

In △ABC, AB = 13.2m, BC = 6.9m and ∠ACB = 90°. H lies on AC such that ∠BHC = 46°. Find (i) ∠ABH (ii) The length of AH

Mathematics
1 answer:
Montano1993 [528]2 years ago
5 0

Answer:

(i) ∠ABH = 14.46⁰

(ii) The length of AH = 4.6 m

Step-by-step explanation:

<u><em>From the image uploaded;</em></u>

Consider △ABC;

the length of b is calculated by applying Pythagoras theorem as follows;

b² = c² - a²

b² = (13.2)² - (6.9)²

b² = 126.63

b = √126.63

b = 11.25 m

Also, ∠ABC is calculated as;

Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o

Consider △CBH, ∠CBH is calculated as;

∠CBH = 90⁰ - 46⁰ = 44⁰

(i) ∠ABH will be calculated as;

∠ABH = θ

θ + 44⁰ = ∠ABC

θ + 44⁰ = 58.46⁰

θ = 58.46⁰  - 44⁰

θ = 14.46⁰

Thus, ∠ABH = 14.46⁰

(ii) The length of AH

length HC is calculated as;

tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m

length of AH = CA - HC

x = b - HC

x = 11.25 - 6.66

x = 4.6 m

length of AH = 4.6 m

You might be interested in
What's 149 rounded to the nearest tenth
alexandr1967 [171]
150 because you round the 4 because the number in the ones place is over 5.
3 0
3 years ago
What are the steps into solving this equation?
zhannawk [14.2K]
First, you must do the parentheses!!!
Next, when you are done solving the parentheses, you will do the outside numbers!!
Then, when doing the outside numbers, you'll combine(doing +, ×, ÷ or -)
And finally, you get your answer!!!

:):):):):)
4 0
3 years ago
A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation
Alexxx [7]
Ok

y=-0.04x^2+8.3x+4.3
when the rocket reaches the ground (when height=0, ie when y=0), then the rocket will land, find the x coordinate

set y=0
0=-0.04x^2+8.3x+4.3
use quadratic formula
if you have ax^2+bx+c=0, then
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}
a=-0.04
b=8.3
c=4.3
x=\frac{-8.3+/- \sqrt{8.3^{2}-4(-0.04)(8.3)} }{2(-0.04)}
x=208.017 or -0.516785
xrepresents horizontal distance
you cannot have a negative horizontal distance unless you fired and theh wind blew it backwards
therefor x=280.017 is the answer
208.02 m


7 0
3 years ago
Helppppppppppppppppppppppp
8_murik_8 [283]

$138.00

Step-by-step explanation:

Steven earns in 4 hours -$23.00

he earns in 6 hours-$34.50

there fore in 10 hours -23.00+34.50=$57.50

in 20 hours -57.50+57.50=$115

and in 4 hours-$23.00+115.00=138.00$

then he earn $138.00 one day

8 0
2 years ago
Jane's family divided up their garden so that 3/4 of the garden will have vegetables. Jane and her sister will plant 3/4 of the
vodka [1.7K]

9/16 of the family garden

We can use an equation to solve this:

(3/4) * (3/4) = (9/16)

8 0
3 years ago
Other questions:
  • Alberto is thinking of buying a jar of fish food flakes that will last 110 days. If he does not change the number of fish, how m
    8·2 answers
  • Which expression has a value of 3/4
    11·1 answer
  • The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of
    6·1 answer
  • Determine if the two triangles are congruent
    13·2 answers
  • HELP ME PLS HURRY PLEASE PLEASE
    12·1 answer
  • !!! HELP ASAP !!! 40 x 20 - 6 + 4 =
    8·1 answer
  • 2. What is the slope of a line that is parallel to the line shown?
    11·2 answers
  • The chart below contains the results of a survey in which students were asked about their cell phone plan.
    10·2 answers
  • As a salesperson, you are paid $150 per week plus $5 per sale that you make. This week
    14·1 answer
  • write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answ
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!