The angles: B = 350, A1 = 230 and h = 3.5cm ;

BD = 3.5/tan(35°)

CD = 3.5*tan(23°)

Area of triangle ABC = 1/2(3.5²/tan(35°) - 3.5²*tan(23°))

$${\mathtt{Area}} = \left({\frac{{{\mathtt{3.5}}}^{{\mathtt{2}}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{35}}^\circ\right)}}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{23}}^\circ\right)}\right) \Rightarrow {\mathtt{Area}} = {\mathtt{6.147\: \!498\: \!292\: \!005\: \!575\: \!7}}$$

Area ≈ 6.147cm².

Area of a triangle ABC = area ABD - area ACD

Area ABC = 8.75cm² - 2.6cm²

Area ABC = ≈6.15cm²

Area of ABC =  (1/2)(BC)(AD) =

(1/2)(3.5 )(3.5)  ≈ 6.125 sq cm

Here's a pic.......

Hello everybody.I am fiora.And I going to do this problem with you all.

First,I think you guys only get part of the answers right.

Now,let me repeat the question, The angles: B = 35o,  A1 = 23o  and   h = 3.5cm ; (The angle  A1 is located between  b and  h ) Find the area of a triangle  ABC.

At first, what is b? b in this question can be the base of the triangle or the opposite side of the angle B.

However, if b is the base of the triangle ,then b is perpendicular (90 degrees) to the h (height),but according to given,the angle between b and h is 23 degrees,so b can not be the base.

Now,b can only be the opposite side of angle B.

Here is my picture of this situations.

  In triangle ABC, the opposite side of angle B is AC

and in triangle ABE,the opposite side of angle B is AE

Look at triangle ABC,area of triangle ABC=1/2(AD*BC)=1/2[AD*(BD-CD)]

BD=AD/tan(7pi/36)  

AD=h is the height of the triangle,so angle ADC=90 degrees

Threfore angle ACD=180 degrees -angle CAD- angle ADC=180 degrees -23 degrees -90 degrees=67 degree

so CD=AD/tan(67pi/180)

so area fo triangle ABC=1/2[AD*(BD-CD)]=

1/2[3.5cm*（3.5cm/tan(7pi/36)-3.5cm/tan67(pi/180)=1/2[3.5cm*3.5128561668618683cm]

=6.14749829200826952 cm^2

In triangle ABE,h (AD) is the height of the triangle 

so angle ADE=90 degrees ,and angle DAE=angle CAD= 23 degree,plus segment AD=segment AD

so triangle CAD is congruent to triangle EAD.

so CD=ED=3.5/tan(7pi/36) (the corresopding sides of congruent triangles are equal) 

area of triangle ABE=1/2*[AD*BE]=1/2[AD*(BD+DE)]=1/2[3.5 cm*(3.5 cm/tan7(pi/36)+3.5 cm/tan(67pi/180)]=11.347314790575381975 cm^2

Here is my graph from desmos.

https://www.desmos.com/calculator/mf39mbkv1i

Is it cool?and Thank You CPhill for correted my mistook.

LOL! You changed your question!.....

Hi Fiora,

Your Desmos graph has spun me out!     

Your graph is brilliant but have you ever tried to use GeoGebra?   

It is heaps easier for this and it is a free download.  

Your GeoGebra diagram is really impressive too CPhill - You are becoming an expert